The locus of a point whose distance from the point $(3,0)$ is $3 / 5$ times its distance from the line $x=p$ is an ellipse with centre at the origin. The value of $p$ is

JEE MATHEMATICS MCQ: ELLIPSE

1 Easy

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Application +4 | -1

The locus of a point whose distance from the point

(3,0)

3 / 5

times its distance from the line

x=p

is an ellipse with centre at the origin. The value of

p

View answer and explanation

Correct option: C

\frac{25}{3}

Option C (

\frac{25}{3}

) is correct because it represents the x-coordinate of the directrix of the ellipse.

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\frac{x^2}{144}+\frac{y^2}{81}=1

m

\mathrm{M}

\mathrm{mM}

P

\frac{{{x^2}}}{{25}} + \frac{{{y^2}}}{{16}} = 1

S

S'.

A

PSS',

A

A

B

(\sqrt{7}, 0)

(-\sqrt{7}, 0)

P

9 x^{2}+16 y^{2}=144

\mathrm{PA}+\mathrm{PB}

\frac{x^2}{a^2}+\frac{y^2}{b^2}=1

r

\frac{x^2}{25}+\frac{y^2}{16}=1

P

x=0

Q

R

Q

y=x

Q

R

N P

Q

P

O