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Equation of Pair of Tangents: Hyperbola

a curve c has...

Question

a curve c has a property that if a tangent at any point, say P, meets the axes at A and B then P is the midpoint of AB if the curve passes through (1,1) find its equation.

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Q. A curve C has the property that if the tangent drawn at any point 'P' on C meets the coordinate axes at A and B, and P is midpoint of AB. If the curve passes through the point

(1, 1)

then the equation of the curve is?

Q. If a curve passing through

(1, 1)

is such that the tangent drawn at any point P on it intersects the x-axis at Q and the reciprocal of abscissa of point P is equal to twice x-intercept of a tangent at P. Then the equation of the curve is

C

passes through origin and has the property that at each point

(x, y)

on it the normal line at that point passes through

(1, 0)

. The equation of a common tangent to the curve

C

and the parabola

y^{2} = 4 x

Q. Assertion(A): If the tangent at any point

P

x y = a^{2}

meets the axes at

A

B

A P : P B = 1 : 1

Reason(R): The tangent at

P (x, y)

X^{m} . Y^{n} = a^{m + n}

meets the axes at

A

B

. Then the ratio of

P

¯ ¯¯¯¯¯¯ ¯ A B

n : m

.

Q. If a curve passing through

(1, 1)

is such that the tangent drawn at any point

P

in it intersects the x-axis at

Q

and the recriprocal of abscissa of point

P

is equal to twice x-intercept of tangent at

P

. Then the equation of the curve is

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Equation of Pair of Tangents: Hyperbola

Standard XII Mathematics

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