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Family whose x and y intercepts of a tangent at any point are respectively double of x and y coordinates of that point is 1) xy=c 2)x^2 + y^2=c 3) x^2 – y^2-c 4) none


Family whose x and y intercepts of a tangent at any point are respectively double of x and y coordinates of that point is


1) xy=c  2)x^2 + y^2=c 3) x^2 – y^2-c  4) none

Grade:12

1 Answers

Jitender Singh IIT Delhi
askIITians Faculty 158 Points
7 years ago
Ans:
Hello Student,
Please find answer to your question below

xy = c^2
For the slope of tangent at (x1, y1)
xy' + y = 0
y' = \frac{-y_{1}}{x_{1}}
Equation of tangent:
(y - y_{1}) = \frac{-y_{1}}{x_{1}}(x-x_{1})
x_{1}y + y_{1}x = 2x_{1}y_{1}
X & Y intercept:
(2x_{1}, 2y_{1})
So intercept is twice the x, y coordinates of the point.

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