Let C: x²+y²=4 and C^(): x²+y²-4 λ x+9=0 be two circles. If the set of all values of λ so that the circles C and C intersect at two distinct points, is R-[a, b], then the point (8 a+12,16 ~b-20) lies on the curve:

Coordinate Geometry: JEE Main 2024 Mathematics question

JEE Main 2024 · 1 Feb, Morning shift · Q3034

JEE Main 20241 Feb, Morning shiftMathematicsMediumCoordinate Geometry478× since 2002

Let

C: x^2+y^2=4

and

C^{\prime}: x^2+y^2-4 \lambda x+9=0

be two circles. If the set of all values of

\lambda

so that the circles

\mathrm{C}

and

\mathrm{C}

intersect at two distinct points, is

\mathrm{R}-[\mathrm{a}, \mathrm{b}]

, then the point

(8 \mathrm{a}+12,16 \mathrm{~b}-20)

lies on the curve :