JEE Main Mathematics: Co-Ordinate Geometry Quiz!

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| By Tanmay Shankar

Tanmay Shankar

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1/10 Questions

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?
- 2 < r < 8
- R = 2
- R < 3
- R > 5

About This Quiz

This JEE Main Mathematics quiz focuses on Coordinate Geometry. It assesses skills through complex problem-solving questions involving line equations, relationships between geometric points, and properties of lines. Ideal for students preparing for engineering entrance exams.

JEE Main Mathematics: Co-ordinate Geometry Quiz! - Quiz

2.

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?
- (4, 3)
- (3, 4)
- (4, 7)
- (7, 4)
Correct Answer

A. (4, 7)
3.

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):
- Are vertices of a triangle
- Lie on parabola
- Lie on a circle
- Lie on a straight line
Correct Answer

A. 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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4.

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

A.
5.

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?
- X + 2 = 0
- 3x – y + 13 = 0
- 3x + 4y =18
- 4x + 3y = 12
Correct Answer

A. 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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6.

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:
- 4/3
Correct Answer

A.
7.

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

A.

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 line y = x meets y = k at: (Given k ≤ 0)
- One point
- Two points
- Three points
- Zero points
Correct Answer

A. Zero points
9.

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

A. Four lines
10.

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

A. 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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Mar 18, 2023

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Aug 26, 2014

Quiz Created by
Tanmay Shankar

JEE Main Mathematics: Co-ordinate Geometry Quiz!

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?

Quiz Preview

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 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:

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?

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:

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

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

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

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 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:

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:

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

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

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