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 $\frac{5 \sqrt{5}}{\sqrt{2}}$