If a normal to the hyperbola xy - c 2 at ct 1- c - t 1 meets the curve again at ct 2- c - t 2 then-A- t1 t2-1B- t2-t1-2-t1C- t23 t1-1D- t13 t2-1

The correct option is D Equation of normal at ( ct_1,c/t_1 )is t_1^3x t_1y ct_1^4 +c =0 It passes through ( ct_2,c/t_2 ) ie.,t_1^3ct_2 t_1 c/t_2 ct_1^ ...

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Byju's Answer

Standard XII

Mathematics

Distance between Parallel Lines

If a normal t...

Question

If a normal to the hyperbola $x y = c^{2}$ at $(c t_{1}, \frac{c}{t_{1}})$ meets the curve again at $(c t_{2}, \frac{c}{t_{2}})$ then:

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Solution

The correct option is D
Equation of normal at $(c t_{1}, \frac{c}{t_{1}}) i s t_{1}^{3} x - t_{1} y - c t_{1}^{4} + c = 0 I t p a s s e s t h r o u g h (c t_{2}, \frac{c}{t_{2}}) i e ., t_{1}^{3} c t_{2} - t_{1} \frac{c}{t_{2}} - c t_{1}^{4} + c = 0 \Rightarrow (t_{1} - t_{2}) (t_{1}^{3} t_{2} + 1) = 0 \Rightarrow t_{1}^{3} t_{2} = - 1$

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If a normal to the hyperbola xy=c2 at (ct1,ct1) meets the curve again at (ct2,ct2) then:

The correct option is D Equation of normal at (ct1,ct1)ist31x−t1y−ct41+c=0It passes through(ct2,ct2)ie.,t31ct2−t1ct2−ct41+c=0⇒(t1−t2)(t31t2+1)=0⇒t31t2=−1

If a normal to the hyperbola $x y = c^{2}$ at $(c t_{1}, \frac{c}{t_{1}})$ meets the curve again at $(c t_{2}, \frac{c}{t_{2}})$ then: