The distance of a point on ellipse x26 + y22 

Subject

Mathematics

Class

JEE Class 12

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

11.

If the algebraic sum of the perpendicular distances from the points (2, 0), (0, 2) and (1, 1) on a variable line is zero, then the line will pass through the fixed point

  • (1, 2)

  • (1, 1)

  • (0, 0)

  • (2, 1)


12.

The locus ofthe point of intersection of the lines xcosα + ysinα = p and xsinα - ycosα = q (α is a variable) will be

  • a circle

  • a staright line

  • a parabola

  • an ellipse


13.

The locus of the mid points of the chords of a circle which subtend a right angle at its centre (equation ofthe circle is x2 + y2 = a2)will be

  • x2 + y2 = 3a2

  • x2 + y2a23

  • 2(x2 + y2) = a2

  • 4(x2 + y2) = a2


14.

If the line 3x - 2y + p = 0 is normal to the circle x2 + y2 = 2x - 4y - 1, then p will be

  • - 5

  • 7

  • - 7

  • 5


Advertisement
15.

If the two circles x2 + y2 = r2 and x2 + y2 - 10x + 16 = 0 intersect at two real points, then

  • 1 < r < 7

  • 3 < r < 10

  • 2 < r < 9

  • 2 < r < 8


16.

The equation of the common tangent to the parabolas y2 = 2x and x2 = 16y will be

  • x + y + 2 = 0

  • x - 3y + 1 = 0

  • x + 2y - 2 = 0

  • x + 2y + 2 = 0


17.

The equation of the tangent to the parabola y2 = 8x, which is parallel to the line 2x - y + 7 = 0, will be

  • y = x + 1

  • y = 2x + 1

  • y = 3x + 1

  • y = 4x + 1


Advertisement

18.

The distance of a point on ellipse x26 + y22 = 1 from its centre is 2. The eccentric angle of the point will be

  • π4 or π3

  • π3 or 3π5

  • π4 or 3π4

  • None of these


C.

π4 or 3π4

Let the eccentric angle ofthe point be 0, then 1ts coordinates are 6cosθ, 2sinθ.

Centre of a given ellipse is (0, 0).

According to the question,

6cosθ - 02 + 2sinθ - 02 = 2 6cos2θ + 2sin2θ = 4 6cos2θ + 21 - cos2θ = 4 4cos2θ = 2  cosθ = ± 12 θ = π4 or 3π4


Advertisement
Advertisement
19.

The distance between the foci of a hyperbola is 16 and its eccentncity is 2. Its equation will be

  • x2 - y2 = 1

  • x2 - y2 = 20

  • x2 - y2 = 4

  • x2 - y2 = 32


20.

The point on x2 = 2y, which is closest to the point (0, 5), will be

  • 22, 0

  • (0, 0)

  • (2, 2)

  • None of these


Advertisement