Question

If the line $2x+5y=12$ intersects the ellipse $4x^2+5y^2=20$ in two distinct points A and B, then the mid point of AB is

• A. $(0,1)$
• B. $(1,2)$
• C. $(1,0)$
• D. $(2,1)$

Answer 1

Answer: (B)

$(1,2)$

$2x+5y=12.....\left(1\right)$

$Ellipse:4x^2+5y^2=20$

The midpoint will lie on the given line

So, satisfying all the option in equation (1), we get

A) $2\left(0\right)+5\left(1\right)=12$ (not true)

B) $2\left(1\right)+5\left(2\right)=12$ (true)

C) $2\left(1\right)+5\left(0\right)=12$ (not true)

D) $2\left(2\right)+5\left(1\right)=12$(not true)