In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line `x+y=2` touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = `6sqrt2` units. The equation of the tangent to the hyperbola at `(-1, 7//2)` isA. `5x+2y=2`B. `3x+2y=4`C. `3x+4y=11`D. none of these

In a hyperbola, the portion of the tangent intercepted between the asy

1.	In a hyperbola, the portion of the tangent intercepted between the asymptotes is bisected at the point of contact. Consider a hyperbola whose center is at the origin. A line `x+y=2` touches this hyperbola at P(1,1) and intersects the asymptotes at A and B such that AB = `6sqrt2` units. The equation of the tangent to the hyperbola at `(-1, 7//2)` isA. `5x+2y=2`B. `3x+2y=4`C. `3x+4y=11`D. none of these
Answer» Correct Answer - B Let the equation of the hyperbola be `2x^(2)+2y^(2)+5xy+lambda=0` It passes through (1,1). Therefore, `2+2+5+lambda=0` `"or "lambda=-9` So, the hyperbola is `2x^(2)+2y^(2)+5xy=9` The equation of the tangent at `(-1,7//2)` is given by `2x(-1)+2y((7)/(2))+5(x(7//2)+(-1)y)/(2)=9` `"or "3x+2y=4`

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