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Equation of Pair of Tangents: Hyperbola

If the line y...

Question

If the line y=mx+1 is tangent to the parabola y²=4x, then find the value of m.

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Solution

Dear student
$G i v e n c u r v e i s y = m x + 1 a n d c u r v e y^{2} = 4 x, s o l v e b o t h s i m l u \tan e o u s l y, w e g e t \Rightarrow {(m x + 1)}^{2} = 4 x \Rightarrow m^{2} x^{2} + (2 m - 4) x + 1 = 0 A s w e k n o w, \tan g e n t t o u c h e s t h e c u r v e, ∴ r o o t s o f a b o v e q u a d r a t i c w i l l b e e q u a l \Rightarrow D = b^{2} - 4 a c = 0 \Rightarrow {(2 m - 4)}^{2} - 4 (m^{2}) (1) = 0 \Rightarrow 4 m^{2} + 16 - 16 m - 4 m^{2} = 0 \Rightarrow m = 1$
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Q. If the line y = mx + 1 is tangent to the parabola y² = 4x, then find the value of m. [NCERT EXEMPLAR]

y = m x + 1

is a tangent to the parabola

y^{2} = 4 x

y = m x + c

is a tangent to the parabola

y^{2} = 4 a (x + a)

y = m x + 1

be a tangent to

y^{2} = 4 x

then find the value of

m

y = m x + c

is tangent to the circle

x^{2} + y^{2} = 5 r^{2}

and the parabola

y^{2} - 4 x - 2 y + 4 λ + 1 = 0

and point of contact of the tangent with the parabola is

(8, 5),

then the value of

(25 r^{2} + λ + 2 m + c)

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Equation of Pair of Tangents: Hyperbola

Standard XII Mathematics

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