Test Index

Parabola Part 1

Section: Mathematics

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Question : 19 of 100

Marks: +1, -0

The tangents at the points

A(1,3)

B(1,-1)

on the parabola

y^{2}-2x-2y=1

meet at the point

P

. Then the area (in unit

{}^2

) of the triangle

PAB

[25-Jul-2022-Shift-2]

4
6
7
8

Solution: 👈: Video Solution

Given curve :

y^{2}-2x-2y=1

.

Can be written as

(y-1)^2=2(x+1)

And, the given information can be plotted as shown in figure

Tangent at

A: 2y-x-5=0

using

T=0\}

Intersection with

y=1

is

x=-3

Hence, point

P

is

(-3,1)

Taking advantage of symmetry

Area of

\triangle PAB = 2 \times \; \frac{1}{2} \times (1-(-3)) \times (3-1)

=8

sq. units

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