Determine whether the statement is true or false. The circle with equation kx2 + ky2 = a2 lies inside the circle with equation x2 + y2 = a2, provided that k < 1.

Answer 1

x² + y² = a² is an equation of the circle with center (0,0) and radius a (Assuming that a > 0).

kx² + ky² = a² can be written as x² + y² = (a/√k)², which is an equation of the circle with center (0,0) and radius a/√k, if 0 < k < 1.

Since 0 < k < 1, 0 < a < a/√k. So, the given statement is FALSE. For example, if k = 1/4, then a/√k = 2a > a.

Answer 2

I'm pretty-sure you mean kx^2 + ky^2 = a^2

within:

x^2+y^2=a^2

You're stating k=1. You see; a=a.

The area of a circle is r^2*π.

It's false.