The circle  x2 + y2 + 4x - 7y + 12 = 0, cuts an intercepton

Previous Year Papers

Download Solved Question Papers Free for Offline Practice and view Solutions Online.

Test Series

Take Zigya Full and Sectional Test Series. Time it out for real assessment and get your results instantly.

Test Yourself

Practice and master your preparation for a specific topic or chapter. Check you scores at the end of the test.
Advertisement

 Multiple Choice QuestionsMultiple Choice Questions

1.

A circle is drawn on the chord of a circle x2 + y2 = a2 as diameter. The chord lies on the line x + y = a. What is the equation of the circle ? 

  • x2 + y2 - ax - ay + a2 = 0

  • x2 + y2 - ax - ay = 0

  • x2 + y2 + ax +ay = 0

  • x2 + y2 +ax + ay - 2a2 = 0


2.

The equation 2x2 - 3y2 - 6 = 0 represents : 

  • a circle

  • a parabola

  • an ellipse 

  • a hyperbola


3.

The two parabolas y2 = 4ax and x2 = 4ay intersect :

  • at two points on the line y = x

  • Only at the origin

  • At three points one of which lies on y + x = 0

  • Only at (4a, 4a)


Advertisement

4.

The circle  x2 + y2 + 4x - 7y + 12 = 0, cuts an intercepton y-axis equal to :

  • 1

  • 3

  • 4

  • 7


A.

1

x2 + y2 + 4x - 7y + 12 = 0Compare with the equation,x2 + y2 +2gx +2fy +c = 0 2g = 4,   g = 2 2f = - 7, f = - 72c = 12Intercept length on y- axis= 2f2 - c= 2 - 722 - 12= 2494 - 12= 2 × 49 - 484= 2 × 12= 1


Advertisement
Advertisement
5.

In a circle of diameter 44 cm, the length of a chord is 22 cm. What is the length of minor arc of the chord ?

  • 48421 cm

  • 24221cm

  • 12121cm

  • 447cm


6.

The sum of the focal distance of a point on an ellipse is constant and equal to the :

  • Length of minor axis

  • Length of major axis

  • Length if latus rectum

  • Sum of the lengths of semi-major and semi-minor axes


7.

For r > 0, f(r) is the ratio of perimeter to area of a circle of radius r. Then f(1) + f(2) = ?

  • 1

  • 2

  • 3

  • 4


8.

The minimum distance from the point (4, 2) to y = 8x is equal to :

  • 2

  • 22

  • 2

  • 32


Advertisement
9.

What is the equation of the ellipse whose vertices are(± 5, 0) and foci are at (± 4, 0) ?

  • x225 + y29 = 1

  • x216 + y29 = 1

  • x225 + y216 = 1

  • x29 + y225 = 1


10.

What is the area of the region bounded the paraoolas y2 = 6(x - 1) and y2 = 3x ?

  • 63

  • 263

  • 463

  • 563


Advertisement