Question

The focal chord to y² =16x is tangent to (x–6)² +y² = 2, then the possible value of the slope of this chord, are

a. {–1, 1}

b. {–2, 2}

c. \(-2,\frac{1}{2}\)

d. \(2,-\frac{1}{2}\)

Answer 1

Correct option is a. {–1, 1}

The focus of parabola is (4, 0). Let slope of focal chord be m. Equation of focal chord is y = m(x–4). It is tangent to the circle then

\(\left|\frac{6m-4m}{\sqrt{m^2+1}}\right|=\sqrt{2}\)

4m² =2(m² +1)

2m² = 2 m = ±1