MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Tangent of a Curve y =f(x)

P1 : y2 = 4ax...

Question

$P_{1} : y^{2} = 4 a x, P_{2} : y^{2} = - 4 a x L : y = x$
Equation of the tangent at a point on the parabola $P_{1}$ where the line $L$ meets the parabola is

A

x - 2 y + 4 a = 0

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

B

x + 2 y - 4 a = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

C

x + 2 y - 8 a = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

D

x - 2 y + 8 a = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $x - 2 y + 4 a = 0$
Clearly $P_{1}$ and $L$ meets at $(4 a, 4 a)$
Thus equation of tangent at this point is given by,
$y (4 a) = 2 a (x + 4 a) \Rightarrow x - 2 y + 4 a = 0$

Suggest Corrections

thumbs-up

0

Similar questions

Q. The common tangent to the parabolas

y^{2} = 4 a x

x^{2} = 32 a y

has the equation

Q. A variable chord

P Q

of the parabola

y^{2} = 4 a x

is drawn parallel to line

y = x

. Then the locus of point of intersection of normals at

P

Q

Q. The equation of the circle passing through points of intersection of the circle

x^{2} + y^{2} - 2 x - 4 y + 4 = 0

x + 2 y = 4

and touches the line

x + 2 y = 0

P_{1} : y^{2} = 4 a x, P_{2} : y^{2} = - 4 a x L : y = x

Area of the rectangle formed by joining the vertices of the latus rectum of the two parabolas

P_{1}

P_{2}

P_{1} : y^{2} = 4 a x, P_{2} : y^{2} = - 4 a x L : y = x

The coordinates of other extremity of a focal chord of the parabola

P_{2}

, one of whose extremity is the point of intersection of

L

P_{2}

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Tangent of a Curve y =f(x)

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon