JEE Main Mathematics: Co-ordinate Geometry Quiz!

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| By Tanmay Shankar
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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
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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

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  • 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?   - ProProfs

    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:  

    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

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

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

    • JEE Main Mathematics: Co-ordinate Geometry Quiz! - Quiz
    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)  - ProProfs

    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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  • Current Version
  • Mar 18, 2023
    Quiz Edited by
    ProProfs Editorial Team
  • Aug 26, 2014
    Quiz Created by
    Tanmay Shankar
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