Question

A circle is drawn to pass through the extremities of the latus rectum of the parabola y² = 8x. If it given the this circle also touches the directrix of the parabola. Radius of this circle is equal to –

• A. 4
• B. $\sqrt{21}$
• C. 3
• D. $\sqrt{26}$

Answer 1

Answer: (A)

4

Answer 2

Extremities of the latus-rectum are (2, 4) and (2, –4). Since any circle drawn with any focal chord as it’s diameter touches the directrix. Thus equation of required circle is

(x – 2)² + (y – 4) (y + 4) = 0, i.e., x² + y² – 4x – 12 = 0, it’s radius is

$\sqrt{4 + 12}$= 4.