Comprehension Based Questions: Conic Sections - Free MCQ Practice Test

PASSAGE 1

Consider the circle x² + y² = 9 and the parabola y² = 8x. They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the curcle 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. (2007 -4 marks)

Q. The ratio of the areas of the triangles PQS and PQR is

PASSAGE 1

Consider the circle x² + y² = 9 and the parabola y² = 8x. They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the curcle 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. (2007 -4 marks)

Q. The radius of the circumcircle of the triangle PRS is (2007 -4 marks)

PASSAGE 1

Consider the circle x² + y² = 9 and the parabola y² = 8x. They intersect at P and Q in the first and the fourth quadrants, respectively. Tangents to the curcle 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. (2007 -4 marks)

Q. The radius of the incircle of the triangle PQR is (2007 -4 marks)

PASSAGE 2

The circle x² + y² – 8x = 0 and hyperbola  intersect atthe points A and B. (2010)

Q. Equation of a common tangent with positive slope to the circle as well as to the hyperbola is

PASSAGE 2

The circle x² + y² – 8x = 0 and hyperbola  intersect atthe points A and B. (2010)

Q. Equation of the circle with AB as its diameter is

PASSAGE 3
Tangents are drawn from the point P(3, 4) to the ellipse  touching the ellipse at points A and B. (2010)

Q. The coordinates of A and B are

PASSAGE 3
Tangents are drawn from the point P(3, 4) to the ellipse  touching the ellipse at points A and B. (2010)

Q. The orthocenter of the triangle PAB is

PASSAGE 3
Tangents are drawn from the point P(3, 4) to the ellipse  touching the ellipse at points A and B. (2010)

Q. The equation of the locus of the point whose distances from the point P and the line AB are equal, is

 PASSAGE 4

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.

Q. Length of chord PQ is (JEE Adv. 2013)

 PASSAGE 4

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet at a point lying on the line y = 2x + a, a > 0.

Q. If chord PQ subtends an angle θ at the vertex of y² = 4ax, then tan q =            (JEE Adv. 2013)

PASSAGE 5
Let a, r, s, t be nonzero real numbers. Let P (at², 2at), Q, R (ar², 2ar) and S (as², 2as) be distinct points on the parabola y² = 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0) (JEE Adv. 2014)

Q. The value of r is

PASSAGE 5
Let a, r, s, t be nonzero real numbers. Let P (at², 2at), Q, R (ar², 2ar) and S (as², 2as) be distinct points on the parabola y² = 4ax. Suppose that PQ is the focal chord and lines QR and PK are parallel, where K is the point (2a, 0) (JEE Adv. 2014)

Q. If st = 1, then the tangent at P and the normal at S to the parabola meet at a point whose ordinate is

PASSAGE 6
Let F₁(x₁, 0) and F₂(x₂, 0) for x1 < 0 and x₂ > 0, be the foci of the ellipse   Suppose a parabola having vertex at the origin and focus at F₂ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant.

Q. The orthocentre of th e triangle F₁MN is (JEE Adv. 2016)

PASSAGE 6
Let F₁(x₁, 0) and F₂(x₂, 0) for x1 < 0 and x₂ > 0, be the foci of the ellipse   Suppose a parabola having vertex at the origin and focus at F₂ intersects the ellipse at point M in the first quadrant and at point N in the fourth quadrant.

Q. If the tangen ts to the ellipse at M an d N meet at R and the normal to the parabola at M meets the x-axis at Q, then the ratio of area of the triangle MQR to area of the quadrilateral MF₁NF₂ is   (JEE Adv. 2016)