The locus of a point whose chord of contact with respect to the circle `x^2+y^2=4` is a tangent to the hyperbola `x y=1` is a/an ellipse (b) circle hy

Question

The locus of a point whose chord of contact with respect to the circle `x^2+y^2=4` is a tangent to the hyperbola `x y=1` is a/an ellipse (b) circle hy

The locus of a point whose chord of contact with respect to the circle `x^2+y^2=4` is a tangent to the hyperbola `x y=1` is a/an ellipse (b) circle hyperbola (d) parabola
A. ellipse
B. circle
C. hyperbola
D. parabola

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Salim Ahmed Kawsar

Correct Answer - C
Let the point be (h, k).
Then the equation of the chord of contact is `hx+ky=4.`
Since `hx+ky=4` is tangent to xy = 1,
`x((4-hx)/(k))=1`
has two equal roots.
Therefore, discriminant of `hx^(2)-4x+k=0` is 0.
`therefore" "hk=4`
Thus, the locus of (h, k) is xy = 4.

4 views Answered 2023-02-05 15:29