JEE Main: Co-ordinate Geometry Exam Quiz!

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| By Tanmay Shankar

Tanmay Shankar

Community Contributor

Quizzes Created: 491 | Total Attempts: 1,782,797

Questions: 10 | Attempts: 117 | Updated: Mar 21, 2023

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Questions and Answers

1.

If the line x = 1/2, is the directrix of a parabola y² – kx + 6 = 0, then which of the following is a value of ‘k’?
- A.
  
  – 4
- B.
  
  – 6
- C.
  
  – 1/4
- D.
  
  – 8
Correct Answer
B. – 6
2.

Equations x = t²+t+1 and y = t² – t +1, represents which of the following curve?
- A.
  
  An ellipse
- B.
  
  A pair of straight
- C.
  
  A hyperbola
- D.
  
  A parabola
Correct Answer
D. A parabola
3.

Angle between tangents drawn from the point (2, 1) to the parabola y² = – 32x is:
- A.
- B.
- C.
- D.
Correct Answer
B.
4.

A parabola has the origin at it focus and the line x = 2 as its directrix. Then the vertex of the parabola will be at:
- A.
  
  (2, 0)
- B.
  
  (0, 2)
- C.
  
  (1, 0)
- D.
  
  (0, 1)
Correct Answer
C. (1, 0)

Explanation
from the diagram it is clear that the vertex will be the midpoint of OP So co-ordinate of vertex are (1, 0)

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5.

The eccentricity of the ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then which of the following correctly represent the equation of ellipse.
- A.
- B.
- C.
- D.
Correct Answer
A.
6.

The number of values of c such that the straight line y = 4x + c touches the curve ;is:
- A.
  
  4
- B.
  
  0
- C.
  
  Infinite
- D.
  
  2
Correct Answer
D. 2
7.

Tangents are drawn to the ellipse at the end of the latus retum. The area of the quadrilateral so formed is:
- A.
  
  54
- B.
  
  27
- C.
  
  27/2
- D.
  
  36
Correct Answer
A. 54
8.

If x = 9 is the chord of the contact of the hyperbola x² – y² = 9, then the equation of the corresponding pair of tangents is
- A.
- B.
- C.
- D.
Correct Answer
B.
9.

2x + √6 y = 2 touches the hyperbola x² – 2y² = 4, then the point of contact is:
- A.
- B.
- C.
  
  Both a & b
- D.
  
  None of these
Correct Answer
C. Both a & b
10.

The eccentricity of hyperbola 3x² – y² = 4 is:
- A.
  
  1
- B.
  
  5
- C.
  
  – 2
- D.
  
  2
Correct Answer
D. 2

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Current Version
Mar 21, 2023

Quiz Edited by
ProProfs Editorial Team
Aug 27, 2014

Quiz Created by
Tanmay Shankar

JEE Main: Co-ordinate Geometry Exam Quiz!

If the line x = 1/2, is the directrix of a parabola y2 – kx + 6 = 0, then which of the following is a value of ‘k’?

Equations x = t2+t+1 and y = t2 – t +1, represents which of the following curve?

Angle between tangents drawn from the point (2, 1) to the parabola y2 = – 32x is:

A parabola has the origin at it focus and the line x = 2 as its directrix. Then the vertex of the parabola will be at:

The eccentricity of the ellipse with its centre at the origin is 1/2. If one of the directrix is x = 4, then which of the following correctly represent the equation of ellipse.

The number of values of c such that the straight line y = 4x + c touches the curve ;is:

Tangents are drawn to the ellipse at the end of the latus retum. The area of the quadrilateral so formed is:

If x = 9 is the chord of the contact of the hyperbola x2 – y2 = 9, then the equation of the corresponding pair of tangents is

2x + √6 y = 2 touches the hyperbola x2 – 2y2 = 4, then the point of contact is:

The eccentricity of hyperbola 3x2 – y2 = 4 is:

If the line x = 1/2, is the directrix of a parabola y² – kx + 6 = 0, then which of the following is a value of ‘k’?

Equations x = t²+t+1 and y = t² – t +1, represents which of the following curve?

Angle between tangents drawn from the point (2, 1) to the parabola y² = – 32x is:

If x = 9 is the chord of the contact of the hyperbola x² – y² = 9, then the equation of the corresponding pair of tangents is

2x + √6 y = 2 touches the hyperbola x² – 2y² = 4, then the point of contact is:

The eccentricity of hyperbola 3x² – y² = 4 is: