Question

If the tangent drawn from the point (-6,9)
to the parabola y2 = kx are perpendicular to
each other, find k.​

Answer 1

value of k = 24

equation of tangent , y = mx + a/m

here, m is slope of tangent of parabola and a = (k/4) [ as standard form of y² = kx = 4(k/4)x, a = (k/4) ]

y = mx + (k/4)/m, is satisfied by (-6,9)

so, 9 = -6m + (k/4)//m

⇒9m = -6m² + (k/4)

⇒6m² + 9m - (k/4) = 0

for tangent to be perpendicular,

m1m2 = -1 ,

i.e., product of roots of 6m² + 9m - (k/4) = 0

-(k/4)/6 = -1

⇒k = 24

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