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Question: If the line ax +by + c = 0 is a tangent to the parabola y<sup>2</sup> – 4y – 8x + 32 = 0, then –...

If the line ax +by + c = 0 is a tangent to the parabola

y2 – 4y – 8x + 32 = 0, then –

A

4b2 = a(7a + 2c + 4b)

B

4b2 = a(7a + c – 4b)

C

4b2 = a(7a + 2c – b)

D

4b2 = a(7a + 2c – b)

Answer

4b2 = a(7a + 2c + 4b)

Explanation

Solution

ax + by + c = 0

y2 – 4y – 8x + 32 = 0

x = – (by+c)a\frac{(by + c)}{a}

y2 – 4y + 8(by+c)a\frac{(by + c)}{a} + 32 = 0

ay2 – 4ay + 8by + 8c + 32 = 0

ay2 + 4y(a – 2b) + 8(c + 4a) = 0

D = 0

16(a – 2b)2 = 4a × 8 (c + 4a) = 0

a2 + 4b2 – 4ab = 2ac + 8a2

4b2 = 7a2 + 2ac + 4ab

4b2 = a(7a + 2c + 4b)