JEE Main Mathematics: Co-ordinate Geometry Quiz!

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| By Tanmay Shankar

Tanmay Shankar

Community Contributor

Quizzes Created: 491 | Total Attempts: 1,781,791

Questions: 10 | Attempts: 119 | Updated: Mar 18, 2023

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Questions and Answers

1.

If a, b, c are related by 9a²+ 16b² – 16c² + 24ab = 0then the greatest distance between any two lines of the family of lines ax + by + c = 0 is:
- A.
  
  4/3
- B.
- C.
- D.
Correct Answer
D.
2.

If a₁, a₂, a₃ as well as b₁, b₂, b₃ are in G.P. with the same common ratio, then the points (a₁, b₁), (a₂, b₂) and (a₃, b₃):
- A.
  
  Are vertices of a triangle
- B.
  
  Lie on parabola
- C.
  
  Lie on a circle
- D.
  
  Lie on a straight line
Correct Answer
D. Lie on a straight line

Explanation
Given, all the three points are related to each other in a way that their common ratios are equal. On calculating the area of the shape formed by these three points, area is found to be zero which means that these three points are collinear.

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3.

What will be the equation of the straight line passing from the point (–3, 5) and making intercept of length between the lines x + 3y +1 = 0 and x + 3y – 1 = 0?
- A.
  
  X + 2 = 0
- B.
  
  3x – y + 13 = 0
- C.
  
  3x + 4y =18
- D.
  
  4x + 3y = 12
Correct Answer
B. 3x – y + 13 = 0

Explanation
The given lines are parallel and the distance between them is 2/√10 which the perpendicular distance between the two is given parallel lines. So the line cutting the given segment must be perpendicular to the x + 3y + 1 = 0 and pass through the point (–3, 5).
Equation of the line is 3(x + 3) – (y – 4) = 0; 3x – y + 13 = 0.

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4.

The line y = x meets y = k at: (Given k ≤ 0)
- A.
  
  One point
- B.
  
  Two points
- C.
  
  Three points
- D.
  
  Zero points
Correct Answer
D. Zero points
5.

The angle between the pair of straight lines y²sin²θ – xysin²θ + x² (cos²θ – 1) = 0 is:
- A.
- B.
- C.
- D.
Correct Answer
D.
6.

The equation: x²y² – 2xy² – 3y² – 4x²y + 8xy + 12y = 0; represents:
- A.
  
  A pair of lines
- B.
  
  A circle and pair of lines
- C.
  
  Four lines
- D.
  
  None of these
Correct Answer
C. Four lines
7.

Circles x² + y² + 2ax + c = 0 and circle x² +y² +2by + c = 0, touches each other then which of the following is correct?
- A.
  
  1/a + 1/b = 1/c
- B.
- C.
- D.
Correct Answer
B.

Explanation
The given equation represents two circles. If the circles touch each other, it means they have a common tangent at the point of contact. The equation of a tangent to a circle is given by the form ax + by + c = 0. Comparing the equations of the circles with the tangent equation, we can see that the coefficients of x and y are the same. Therefore, we can equate the coefficients of x and y in the two circle equations. By doing so, we get 1/a + 1/b = 1/c.

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8.

The number of common tangents to the circle x² + y² – 4 = 0 and x² + y² – 6x – 8y – 24 = 0 is:
- A.
  
  0
- B.
  
  1
- C.
  
  3
- D.
  
  ∞
Correct Answer
C. 3

Explanation
From the two equations C1C2 = 3√10; which is equal to the sum of the two radius of the given circle, it means that the two circles touch each other externally which means that both the circles will have one common tangent and as they are touching each other externally then there will be two more tangents which will touch these

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9.

If the two circles x² + y² = r² and x² + y² – 10x + 16 = 0 intersect each other at some real and distinct points then which of the following is true?
- A.
  
  2 < r < 8
- B.
  
  R = 2
- C.
  
  R < 3
- D.
  
  R > 5
Correct Answer
A. 2 < r < 8
10.

Lines x² – 8x + 12 = 0 and y² – 14y + 45 = 0 form a square. What will be the center of the circle inscribed in the square?
- A.
  
  (4, 3)
- B.
  
  (3, 4)
- C.
  
  (4, 7)
- D.
  
  (7, 4)
Correct Answer
C. (4, 7)

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Current Version
Mar 18, 2023

Quiz Edited by
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Aug 26, 2014

Quiz Created by
Tanmay Shankar

JEE Main Mathematics: Co-ordinate Geometry Quiz!

If a, b, c are related by 9a2 + 16b2 – 16c2 + 24ab = 0then the greatest distance between any two lines of the family of lines ax + by + c = 0 is:

If a1, a2, a3 as well as b1, b2, b3 are in G.P. with the same common ratio, then the points (a1, b1), (a2, b2) and (a3, b3):

What will be the equation of the straight line passing from the point (–3, 5) and making intercept of length between the lines x + 3y +1 = 0 and x + 3y – 1 = 0?

The line y = x meets y = k at: (Given k ≤ 0)

The angle between the pair of straight lines y2sin2θ – xysin2θ + x2 (cos2θ – 1) = 0 is:

The equation: x2y2 – 2xy2 – 3y2 – 4x2y + 8xy + 12y = 0; represents:

Circles x2 + y2 + 2ax + c = 0 and circle x2 +y2 +2by + c = 0, touches each other then which of the following is correct?

The number of common tangents to the circle x2 + y2 – 4 = 0 and x2 + y2 – 6x – 8y – 24 = 0 is:

If the two circles x2 + y2 = r2 and x2 + y2 – 10x + 16 = 0 intersect each other at some real and distinct points then which of the following is true?

Lines x2 – 8x + 12 = 0 and y2 – 14y + 45 = 0 form a square. What will be the center of the circle inscribed in the square?

If a, b, c are related by 9a²+ 16b² – 16c² + 24ab = 0then the greatest distance between any two lines of the family of lines ax + by + c = 0 is:

If a₁, a₂, a₃ as well as b₁, b₂, b₃ are in G.P. with the same common ratio, then the points (a₁, b₁), (a₂, b₂) and (a₃, b₃):

The angle between the pair of straight lines y²sin²θ – xysin²θ + x² (cos²θ – 1) = 0 is:

The equation: x²y² – 2xy² – 3y² – 4x²y + 8xy + 12y = 0; represents:

Circles x² + y² + 2ax + c = 0 and circle x² +y² +2by + c = 0, touches each other then which of the following is correct?

The number of common tangents to the circle x² + y² – 4 = 0 and x² + y² – 6x – 8y – 24 = 0 is:

If the two circles x² + y² = r² and x² + y² – 10x + 16 = 0 intersect each other at some real and distinct points then which of the following is true?

Lines x² – 8x + 12 = 0 and y² – 14y + 45 = 0 form a square. What will be the center of the circle inscribed in the square?