ParabolaHardBloom L3
Question
Tangents are drawn from the points on the line $x - y + 3 = 0$ to parabola $y^{2} = 8x$. Then the variable chords of contact pass through a fixed point whose co-ordinates are :
Options
A.$(3,2)$
B.$(2,4)$
C.$(3,4)$
D.$(4,1)$
Solution
Sol. [Key Concept: The chord of contact of $(x_{1},y_{1})$ on $y^{2} = 8x$ is ${yy}_{1} = 4(x + x_{1})$; as the point runs along the given line, the chord passes through a fixed point.]
Equation of $AB$ is $y(\lambda + 3) = 4(x + \lambda)$
$$\Rightarrow (3y - 4x) + \lambda(y - 4) = 0 $$represents family of lines passing through $(3,4)$
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