Question

$x^2+y^2+2x+4y-20=0$ and $x^2+y^2+6x-8y+10=0$ are the given circles. Which one of the following is correct?

• A. They intersect orthogonally and will have two common tangents. The length of their common chord is $\frac{5\sqrt{5}}{\sqrt{2}}$
• B. Tliey intersect at right angles and will have two common tangents. The length of their common chord is 2
• C. They do not intersect orthogonally and will have three common tangents. The length of their direct common tangent is 5.
• D. They touch each other internally and will have only one common tangent.

Answer 1

Answer: (A)

Correct answer is (a) They intersect orthogonally and will have two common tangents. The length of their common chord is $\frac{5\sqrt{5}}{\sqrt{2}}$