JEE MATHEMATICS MCQ: ELLIPSE

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Application +4 | -1

The line

x = a{t^2}

meets the ellipse

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

in the real points, if

View answer and explanation

Correct option: B

\left| t \right| \le 1

Option B (

\left| t \right| \le 1

) is correct because it ensures that the value inside the square root for calculating y is non-negative, resulting in real points of intersection.

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

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\mathrm{mM}

P

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

S

S'.

A

PSS',

A

A

B

(\sqrt{7}, 0)

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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

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y=x

Q

R

N P

Q

P

O