Parabola Test

Result

Parabola Test - 5

Score
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Rank
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TIME Taken - -

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Question 1
1 / -0

If the normal at a point P on a parabola passes through its focus, then P is

A
a vertex of the parabola

B
an end of a focal chord

C
an end of the latus rectum

D
None of these

Solution

Equation of a normal to the parabola y² = 4ax is y = mx – 2am – am³. It passes through the focus (a, 0) if m = 0 and the point P(0, 0) is the vertex.
Question 2
1 / -0

Let L be a normal to the parabola y² = 4x. If L passes through the point (9, 6), then L is not given by

A
y – x + 3 = 0

B
y + 3x – 33 = 0

C
y + x – 15 = 0

D
y – 2x + 12 = 0

Solution

The equation of normal to the parabola y² = 4ax in slope form is y = mx - 2am - am^3.

So, the equation of normal to the parabola y² = 4x is y = mx – 2m – m³.

As it passes through (9, 6), we get

6 = 9m – 2m – m³

^⇒m³ – 7m + 6 = 0

^⇒m = 1, 2, –3

This shows that L is not given by option (3).