Question

If $A=\left\{\right(x,y):x^2+y^2=25\}$ and $B=\left\{\right(x,y):x^2+9y^2=144\}$, then $A\cap B$ contains

• A. One point
• B. Three points
• C. Two points
• D. Four points

Answer 1

The correct option is D Four points

A=Set of all points (x,y), which lie on the circle:$x^2+y^2=25=5^2$
B=Set of all points (x,y), which lie on the ellipse:$\frac{x^2}{{12}^2}+\frac{y^2}{4^2}=1$

Clearly,$A\cap B$ consists of four points.
Note: Plot the figures in the Cartesian co-ordinate and visualize.