Conic Sections Test

Result

Conic Sections Test - 8

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Weekly Quiz Competition

Question 1
1 / -0

In an ellipse the distance between its foci is 6 and its minor axis is 8 ; the eccentricity of the ellipse is

A
1/√52

B
3/5

C
3/5

D
1/2

Solution

here c=3, b=4, from relation a²=b²+c² we get a=5.

e=c/a = 3/5
Question 2
1 / -0

At what point on the parabola y² = 4x,, the normal makes equal angles with the axes ?

A
(9, 6)

B
(1, - 2)

C
(4, -4)

D
(4, 4)

Solution

If the normal has slope - 1 then the tangent, that is perpendicular to the normal, will have slope = + 1

Hence its equation is y = x+k

Hence the point of intersection between the parabola and the normal is

(x+k)² = 4x

i.e; x² +2kx -4x + k² = 0

For discriminant value to be zero (b² - 4ac) = 0

(2k-1)² -4k² = 0

on solving this we get k = 1

Therefore the equaiton is x² - 2x + 1 = 0

This implies x = 1 and y = ±2
Question 3
1 / -0

The locus of a point which moves so that its distance from a fixed point, called focus, bears a constant ratio, which is less than unity, to its distance from a fixed line, called the directrix is called

A
a parabola

B
a circle

C
a hyperbola

D
an ellipse

Solution

For an ellipse e < 1