Question

Find the equation of tangent at extremities of focal chord through point (3,6) of parabola y²=12x and hence find the area of ∆ formed by this tangent and tangent at vertex​

Answer 1

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Equation of Tangent at A

$yy_1=2a(x+x_1) \\ \implies y\times 6=2\times 3(x+3) \\ \implies \boxed{y=x+3} \longleftarrow \huge\boxed{1}$

Equation of Tangent at B

$y\times (-6) = 2\times3x+3) \\ \implies \boxed{y=-x-3} \longleftarrow \huge\boxed{2} \\ P(3,0)\: and \: Q(0,-3) and \:From\: \boxed{1} \:and \: \boxed{2} R(0,-3)\\ \\ So PQ=6 (By\:Distance\: Formula ) \\ \implies Area of Tria ngle\\ \implies \dfrac{1}{2} \times 3\times 6 \\ \huge\leadsto\boxed{\boxed{Area = 9}}$

Answer 2

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Equation of Tangent at A

$yy_1=2a(x+x_1) \\ \implies y\times 6=2\times 3(x+3) \\ \implies \boxed{y=x+3} \longleftarrow \huge\boxed{1}$

Equation of Tangent at B

$y\times (-6) = 2\times3x+3) \\ \implies \boxed{y=-x-3} \longleftarrow \huge\boxed{2} \\ P(3,0)\: and \: Q(0,-3) and \:From\: \boxed{1} \:and \: \boxed{2} R(0,-3)\\ \\ So PQ=6 (By\:Distance\: Formula ) \\ \implies Area of Tria ngle\\ \implies \dfrac{1}{2} \times 3\times 6 \\ \huge\leadsto\boxed{\boxed{Area = 9}}$