If y = mx + 4 is common tangent to parabolas y2 = 4x and x2 = 2by. T

1.	If y = mx + 4 is common tangent to parabolas y2 = 4x and x2 = 2by. Then value of b is(1) -64(2) -32(3) -128(4) 16
Answer» Answer is (3) y = mx + 4 ……(i) y² = 4x tangent y = mx + a/m ⇒ y = mx + 1/m .....(ii) from (i) and (ii) 4 = 1/m ⇒ m = 1/4 So line y = 1/4x + 4 s also tangent to parabola x² = 2by, so solve and D = 0 x² = 2b(x + 16/4) ⇒ 2x² – bx – 16b = 0 ⇒ D = 0 ⇒ b² – 4 × 2 × (–16b) = 0 ⇒ b² + 32 × 4b = 0 b = –128, b = 0 (not possible)

If y = mx + 4 is common tangent to parabolas y2 = 4x and x2 = 2by. Then value of b is(1) -64(2) -32(3) -128(4) 16

Answer»

Answer is (3)

y = mx + 4 ……(i)

y² = 4x tangent y = mx + a/m

⇒ y = mx + 1/m .....(ii)

from (i) and (ii)

4 = 1/m ⇒ m = 1/4

So line y = 1/4x + 4 s also tangent to parabola

x² = 2by, so solve and D = 0

x² = 2b(x + 16/4)

⇒ 2x² – bx – 16b = 0 ⇒ D = 0

⇒ b² – 4 × 2 × (–16b) = 0

⇒ b² + 32 × 4b = 0

b = –128, b = 0 (not possible)

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If y = mx + 4 is common tangent to parabolas y2 = 4x and x2 = 2by. Then value of b is(1) -64(2) -32(3) -128(4) 16

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