CAT Exam  >  CAT Tests  >  Level-wise Tests for CAT  >  Test Level 3: Coordinate Geometry - CAT MCQ

Test Level 3: Coordinate Geometry - CAT MCQ


Test Description

10 Questions MCQ Test Level-wise Tests for CAT - Test Level 3: Coordinate Geometry

Test Level 3: Coordinate Geometry for CAT 2024 is part of Level-wise Tests for CAT preparation. The Test Level 3: Coordinate Geometry questions and answers have been prepared according to the CAT exam syllabus.The Test Level 3: Coordinate Geometry MCQs are made for CAT 2024 Exam. Find important definitions, questions, notes, meanings, examples, exercises, MCQs and online tests for Test Level 3: Coordinate Geometry below.
Solutions of Test Level 3: Coordinate Geometry questions in English are available as part of our Level-wise Tests for CAT for CAT & Test Level 3: Coordinate Geometry solutions in Hindi for Level-wise Tests for CAT course. Download more important topics, notes, lectures and mock test series for CAT Exam by signing up for free. Attempt Test Level 3: Coordinate Geometry | 10 questions in 20 minutes | Mock test for CAT preparation | Free important questions MCQ to study Level-wise Tests for CAT for CAT Exam | Download free PDF with solutions
Test Level 3: Coordinate Geometry - Question 1

Radius of the circle passing through the foci of the ellipse x2/16 + y2/9 = 1 and having its centre at (0, 3) is

Detailed Solution for Test Level 3: Coordinate Geometry - Question 1

For the given ellipse a2 = 16 and b2 = 9
⇒ a2(1 - e2) = 9
⇒ 16 - a2e2 = 9
⇒ ae = √7
So, foci are at (- √7, 0) and (√7, 0).
Hence, required length of radius 

Test Level 3: Coordinate Geometry - Question 2

If D (2, 1), E (-1, -2) and F (3, 3) are the mid-points of the sides BC, CA and AB, respectively, of the triangle ABC, then the equation of AB is

Detailed Solution for Test Level 3: Coordinate Geometry - Question 2

As the slope of AB is equal to the slope of DE, i.e. 1, so the equation of line AB is x = y ⇒ x - y = 0.

1 Crore+ students have signed up on EduRev. Have you? Download the App
Test Level 3: Coordinate Geometry - Question 3

ABC is an isosceles triangle. If the coordinates of the ends of the base are B (1, 3) and C (-2, 7), then the coordinates of vertex A are

Detailed Solution for Test Level 3: Coordinate Geometry - Question 3

The vertex A (x, y) is equidistant from B and C because ABC is an isosceles triangle.
Therefore, (x - 1)2 + (y - 3)2 = (x + 2)2 + (y - 7)2
⇒ 6x - 8y + 43 = 0
Now, from the options, we have
x = 5/6 and y = 6, which satisfy the above equation.

Test Level 3: Coordinate Geometry - Question 4

If the points (2a, a), (a, 2a) and (a, a) enclose a triangle of area 2 sq. units, then the value of a is

Detailed Solution for Test Level 3: Coordinate Geometry - Question 4

The diagrammatic representation of the same is as shown in the diagrams below.


In either case,

or a2 = 4 or a = ± 2
As -2 is the only option available, a = -2
Hence, answer option 1 is correct.

Test Level 3: Coordinate Geometry - Question 5

In which of the following equations are x and y intercepts not consecutive numbers?  

Detailed Solution for Test Level 3: Coordinate Geometry - Question 5

Option (1):

4 and 5 are intercepts.
Option (2):

6 and 7 are intercepts.
Option (3):

4 and 3 are the intercepts.

Option (4):

19 and 10 are not consecutive.
So, option 4 is correct.

Test Level 3: Coordinate Geometry - Question 6

If 4x - 3y + k = 0 represents a tangent to the circle x2 + y2 = 144, then what is the value of k?

Detailed Solution for Test Level 3: Coordinate Geometry - Question 6


The perpendicular distance OP is given by the formula: 

Also, (x, y) = (0, 0)
⇒ k = ± 60

Test Level 3: Coordinate Geometry - Question 7

Find the area enclosed by |x| + |y| = 4.

Detailed Solution for Test Level 3: Coordinate Geometry - Question 7


The four possible lines are:
x + y = 4; x - y = 4; - x - y = 4 and -x + y = 4
The four lines can be represented on the coordinate axes as shown in the figure.
Thus, a square is formed with the vertices as shown.
The side of the square is  

The area of the square is (4√2)2 = 32 sq. units.

Test Level 3: Coordinate Geometry - Question 8

What is the equation of the line parallel to the line x + 3y = -7 and passing through the centroid of the triangle formed by the intersection of the lines 3x - 4y = -11, 3x - y = -5 and 3x + 2y = 19?

Detailed Solution for Test Level 3: Coordinate Geometry - Question 8

Slope of the line x + 3y = -7 is -1/3.
On solving the equation for the three lines, we get the vertices of the triangles as (-1, 2), (3, 5) and (1, 8).
So, the centroid of the triangle is ([-1 + 3 + 1] / 3, [2 + 5 + 8] / 3) or (1, 5) 
Using the slope-point form of the equation of a line, we get the required equation: y - 5 = (-1/3)(x - 1), i.e. x + 3y = 16.

Test Level 3: Coordinate Geometry - Question 9

Two sides of a square lie on the lines x + y = 1 and x + y + 2 = 0. What is its area ?

Detailed Solution for Test Level 3: Coordinate Geometry - Question 9

The equations of parallel sides of the square are x + y − 1 = 0 and x + y + 2 = 0.
Therefore, Length of the side of the square = Distance between parallel side =

Hence, area of the square = (side)2 = 9/2 sq.units

Test Level 3: Coordinate Geometry - Question 10

The area of triangle formed by the points (p, 2 − 2p),(1 − p, 2p) and (−4 −p, 6 − 2p) is 70 sq. units. How many integral values of p are possible ?

Detailed Solution for Test Level 3: Coordinate Geometry - Question 10

Given the points of triangle, A(p, 2 − 2p),B(1 − p, 2p) and C(−4 − p ,6 − 2p)
Area = 70sq.unit

{p[2p−6+2p]+(1−p)[6−2p+2p]+(−4−p)[2−2p−2p]}=140
p(4p−6)+(1−p)(4)−[(4+p)(2−4p)] =140
4p2 −6p+4−4p−[8−16p+2p−4p2] =140
4p2 −6p+4−4p−8+16p−2p+4p2 =140
8p2 +4p−144=0
2p2 +p−36=0
2p2 +9p−8p−36=0
p(2p+9)−4(2p+9)=0
(2p+9)=0,(p−4)=0
p = −9/2,p = 4
∴ Only one integral value is possible.

5 docs|272 tests
Information about Test Level 3: Coordinate Geometry Page
In this test you can find the Exam questions for Test Level 3: Coordinate Geometry solved & explained in the simplest way possible. Besides giving Questions and answers for Test Level 3: Coordinate Geometry , EduRev gives you an ample number of Online tests for practice

Top Courses for CAT

Download as PDF

Top Courses for CAT