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Mathematics - Parabola Question with Solution | TestHub

MathematicsParabolaTangent to ParabolaMedium2 minQB

MathematicsMediummultiple choice

If two distinct tangents to $y^{2} = 4 a x$ are normals to $x^{2} + y^{2} - 2 αx - 2 b y + c = 0$ , which conditions hold?

Options:(select one or more)

Answer:

B, C

Solution:

A tangent $y = m x + a / m$ must pass through the circle centre $(α, b)$ , so $α m^{2} - bm + a = 0$ . Two distinct real roots require $b^{2} > 4 a α$ , equivalently $α < b^{2} / (4 a)$ ; with the stated symmetric range, C holds.

Stream:JEESubject:MathematicsTopic:ParabolaSubtopic:Tangent to Parabola

⏱ 2mℹ️ Source: QB

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