Ellipse- 3 - Free MCQ Practice Test with solutions, JEE Maths
MCQ Practice Test & Solutions: Test: Ellipse- 3 (30 Questions)
You can prepare effectively for JEE Mathematics (Maths) for JEE Main & Advanced with this dedicated MCQ Practice Test (available with solutions) on the important topic of "Test: Ellipse- 3". These 30 questions have been designed by the experts with the latest curriculum of JEE 2026, to help you master the concept.
Test Highlights:
- - Format: Multiple Choice Questions (MCQ)
- - Duration: 60 minutes
- - Number of Questions: 30
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An ellipse having foci at (3,3) and (-4,4) and passing though the origin has eccentricity equal to
Detailed Solution: Question 1
The length of the major axis of the ellipse (5x - 10)2 + (5y + 15)2 
Detailed Solution: Question 2
from focus to directrix is 
The eccentric angle of a point on the ellipse 
at a distance of 5/4 units from the focus on the positive x-axis, is
at a distance of 5/4 units from the focus on the positive x-axis, is Detailed Solution: Question 3
From any point P lying in first quadrant on the ellipse 
PN is drawn perpendicular to the major axis and produced at Q so that NQ equals to PS, where S is a focus. Then the locus of Q is
PN is drawn perpendicular to the major axis and produced at Q so that NQ equals to PS, where S is a focus. Then the locus of Q is Detailed Solution: Question 4
If a tangent of slope 2 of the ellipse 
is normal to the circle x2 + y2 + 4x + 1 = 0 , then the maximum value of ab is
is normal to the circle x2 + y2 + 4x + 1 = 0 , then the maximum value of ab isDetailed Solution: Question 5
be the tangent
An ellipse has the points (1, -1) and (2, -1) as its foci and x +y - 5 = 0 as one of its tangents. Then the point where this line touches the ellipse is
Detailed Solution: Question 6
From point P (8, 27) , tangent PQ and PR are drawn to the ellipse 
Then the angle subtended by QR at origin is
Then the angle subtended by QR at origin is Detailed Solution: Question 7
An ellipse is sliding along the co-ordinate axes. If the foci of the ellipse are (1,1) and (3,3), then area of the director circle of the ellipse (in sq. units) is
Detailed Solution: Question 8
The equation of the ellipse whose axes are coincident with the co-ordinates axes and which touches the straight lines 3x - 2y - 20 = 0 and x + 6y - 20 = 0 is
Detailed Solution: Question 9
......(i)
......(ii)
is tangent to the ellipse, therefore comparing with eq. …(i)
Number of point on the ellipse 
from which pair of perpendicular tangents are drawn to the ellipse 
from which pair of perpendicular tangents are drawn to the ellipse Detailed Solution: Question 10
at 4 pointsIf maximum distance of any point on the ellipse x2 + 2y2 + 2xy = 1 from its centre be r, then r is equal to
Detailed Solution: Question 11
The equation of the line passing through the centre and bisecting the chord 7x +y -1 = 0 of the ellipse 
Detailed Solution: Question 12
Eccentricity of ellipse 
such that the line joining the foci subtends a right angle only at two points on ellipse, is
such that the line joining the foci subtends a right angle only at two points on ellipse, isDetailed Solution: Question 13
The tangent at the point ‘a’ on the ellipse 
meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity ‘e’ of the ellipse is given by the equation :
meets the auxiliary circle in two points which subtends a right angle at the centre, then the eccentricity ‘e’ of the ellipse is given by the equation :Detailed Solution: Question 14
The number of values of c such that the straight line y = 4x+ c touches the curve 
Detailed Solution: Question 15
If tangents are drawn to the ellipse x2 + 2y2 = 2, then the locus of the midpoint of the intercept made by the tangent between the coordinate axes is
Detailed Solution: Question 16
An ellipse with major and minor axes, 6√3 and 6 respectively slides along the coordinate axes and always remains confined in the first quadrant. If the length of arc described by the centre of the ellipse is 
then the value of k is
then the value of k isConsider the ellipse 
and the parabola y2 = 2x. They intersect at P and Q in the first and fourth quadrants respectively. Tangents to the ellipse at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S. If the area of quadrilateral PQRS, is λ then 
and the parabola y2 = 2x. They intersect at P and Q in the first and fourth quadrants respectively. Tangents to the ellipse at P and Q intersect the x-axis at R and tangents to the parabola at P and Q intersect the x-axis at S. If the area of quadrilateral PQRS, is λ then Detailed Solution: Question 18
The area of the quadrilateral formed by the tangents at the end points of latus rectum of the ellipse 
is k then k/9 is
is k then k/9 isThe length of the focal chord of the ellipse 
which is inclined to x – axis at an angle 45° is λ, then 
which is inclined to x – axis at an angle 45° is λ, then Q is a point on the auxiliary circle corresponding to the point P of the ellipse 
If T is the foot of the perpendicular dropped from the focus S on to the tangent to the auxiliary circle at Q then the ΔSPT is :
If T is the foot of the perpendicular dropped from the focus S on to the tangent to the auxiliary circle at Q then the ΔSPT is :Detailed Solution: Question 21
Let x and y satisfy the relation x2 + 9y2 - 4x + 6y + 4 = 0, then maximum value of the expression (4x - 9y),
Detailed Solution: Question 22
A rectangle ABCD has area 200 square units. An ellipse with area 200π passes through A and C and has foci at B and D, then
A tangent to the ellipse 
at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point is
at any point P meet the line x = 0 at a point Q. Let R be the image of Q in the line y = x, then circle whose extremities of a diameter are Q and R passes through a fixed point. The fixed point isDetailed Solution: Question 24
If the curve x2 + 3y2 = 9 subtends an obtuse angle at the point (2α, α), then a possible value of α2 is
Detailed Solution: Question 25
whose director circle is x2 + y2 = 12. For the required condition (2α, α) should lie inside the circle and outside the ellipse i.e., 
Let S = 0 be the equation of reflection of 
about the line x – y – 2 = 0. Then the locus of point of intersection of perpendicular tangents of S is
about the line x – y – 2 = 0. Then the locus of point of intersection of perpendicular tangents of S isDetailed Solution: Question 26
Any ordinate MP of a ellipse 
meets the auxiliary circle in Q, then locus of point of intersection of normals at P and Q to the respective curves, is
meets the auxiliary circle in Q, then locus of point of intersection of normals at P and Q to the respective curves, isDetailed Solution: Question 27
The radius of the largest circle whose centre at (-3,0) and is inscribed in the ellipse 16x2 + 25y2 = 400 is
The line passing through the extremely A of the major axis and extremity B of the minor axis of the ellipse x2 + 9y2 = 9 meets its auxiliary circle at the point M . Then the area of the triangle with vertices at A,M and the origin O is
Detailed Solution: Question 29
Coordinate of the vertices B and C of triangle ABC are respectively (2, 0) and (8, 0). The vertex ‘A’ is varying in such a way that 
Then the locus of ‘A’ is an ellipse whose major axis is of length.
Then the locus of ‘A’ is an ellipse whose major axis is of length. Detailed Solution: Question 30
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