Question

DO THIS I WILL MARK U BRAINLIEST ..........................................................................
locus of pt of intersection of tangents drawn at the extremities of the normal chord of the hyperbola x²/a² - y²/ b² = 1

Answer 1

WER

Fact: Equation of tangent to the parabola y

2

=4ax at t is given by, ty=x+at

2

Thus equation of tangent to the parabola at t

1

and t

2

are given by,

t

1

y=x+at

1

2

.......(1)

and t

2

y=x+at

2

2

.......(2)

Subtract (2) from (1)

t

1

y−t

2

y=at

1

2

−at

2

2

⇒y(t

1

−t

2

)=a(t

1

+t

2

)(t

1

−t

2

)

⇒y=a(t

1

+t

2

)

Substitute value of y in (1)

⇒at

1

(t

1

+t

2

)=x+at

1

2

⇒x=at

1

t

2

Hence the point of intersection is (at

1

t

2

,a(t

1

+t

2

))

Answer 2

ʰᵉʳᵉ'ˢ ʸᵒᵘʳ ᵃⁿˢʷᵉʳ ⁱⁿ ᵗʰᵉ ᵍⁱᵛᵉⁿ ᵃᵗᵗᵃᶜʰᵐᵉⁿᵗ

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