For different values of a, the locus of the point of intersection

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

111.

The locus of the passes through (a, 0), (- a, 0) is the centre of a circle which two variable points

  • x = 1

  • x + y = a

  • x + y = 2a

  • x = 0


112.

The intercept on the line y = x by the circle x2 = y2 - 2x = 0 is AB. Equation of the circle with AB as the diameter is

  • x2 + y2 = 1

  • x(x - 1) + y(y - 1) = 0

  • x2 + y2 = 2

  • (x - 1)(x - 2) + (y - 1)(y - 2) = 0


113.

If the coordinates of one end of a diameter of the circle x2 + y+ 4x-8y + 5 = 0 are (2, 1), the coordinates of the other end are

  • (- 6, - 7)

  • (6 , 7)

  • (- 6, 7)

  • (7, - 6)


114.

The locus of the middle points of all chords of the parabola y2 = 4ax passing through the vertex is

  • a straight line

  • an ellipse

  • a parabola

  • a circle


Advertisement

 Multiple Choice QuestionsShort Answer Type

115.

Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is - 12, 12


 Multiple Choice QuestionsMultiple Choice Questions

116.

If t1 and t2 be the parameters of the end points of a focal chord for the parabola y2 = 4ax, then which one is true?

  • t1t2 = 1

  • t1t2 = 1

  • t1t2 = - 1

  • t1 + t2 = - 1


117.

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

  • 14

  • 13

  • 12

  • 23


Advertisement

118.

For different values of a, the locus of the point of intersection of the two straight lines 3x - y - 43α = 0 and 3αx + αy - 43 = 0

  • a hyperbola with eccentricity 2

  • an ellipse with eccentricity 23

  • a hyperbola with eccentricity 1916

  • an ellipse with eccentricity 34


A.

a hyperbola with eccentricity 2

Given, 3x - y - 43α = 0 3x - y = 43α         ...(i)and    x3α +αy - 43 = 0                      3x +y = 43α         ...(ii)On multiplying Eq. (i) by Eq. (ii) 3x2 - y2 = 48x216 - y248 = 1which is hyperbola.Hence, eccentricity,e = 48 +1616 = 2


Advertisement
Advertisement
119.

The circles x2 + y2 - 10x + 16 = 0 and x2 + y2 = a2 intersect at two distinct points, if

  • a < 2

  • 2 < a < 8

  • a > 8

  • a = 2


120.

For the two circles x2 + y2 = 16 and x2 + y2 - 2y = 0 there is/are

  • one pair of common tangents

  • only one common tangent

  • three common tangents

  • no common tangent


Advertisement