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Circle question

2025 · 4 Apr · Shift 1 · Q46

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JEE Main
Mathematics
Circle
2025 · 4 Apr · Shift 1 · Q46

Circle question

2025 · 4 Apr · Shift 1 · Q46

JEE MainMathematicsCircleNumerical+4 / −1

Let

C

be the circle

x^2+(y-1)^2=2, E_1

and

E_2

be two ellipses whose centres lie at the origin and major axes lie on x -axis and y -axis respectively. Let the straight line

x+y=3

touch the curves

C, E_1

and

E_2

at

P\left(x_1, y_1\right), Q\left(x_2, y_2\right)

and

R\left(x_3, y_3\right)

respectively. Given that

P

is the mid point of the line segment

Q R

and

P Q=\frac{2 \sqrt{2}}{3}

, the value of

9\left(x_1 y_1+x_2 y_2+x_3 y_3\right)

is equal to

\underline{\hspace{2cm}}

.

Numerical answer

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