JEE MATHEMATICS MCQ: ELLIPSE

1 Easy

1 of 1

Application +4 | -1

The area of the triangle formed by three points on the ellipse

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

whose eccentric angles are

\alpha ,\beta

and

\gamma

View answer and explanation

Correct option: C

2ab\sin \frac{{\alpha - \beta }}{2}\sin \frac{{\beta - \gamma }}{2}\sin \frac{{\gamma - \alpha }}{2}

Option C (

2ab\sin \frac{{\alpha - \beta }}{2}\sin \frac{{\beta - \gamma }}{2}\sin \frac{{\gamma - \alpha }}{2}

) is correct because it represents the area of the triangle formed by the given points on the ellipse using eccentric angles.

More Questions from 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