42.A curve y=f(x) passes through point P(1,1).the normal to curve at point P is a(y-1)+(x-1)=0. If slope of tangent at any point on curve is proportional to ordinate at that pont, then equation of curve is

Open in App

Solution

Suggest Corrections

Similar questions

Q. A curve

y = f (x)

passes through the point

P (1, 1) .

The normal to the curve at

P

(y - 1) + (x - 1) = 0.

If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is:

Q. The slope of the tangent to the curve at any point is the reciprocal of twice the ordinate at that point. The curve passes through the point (4, 3). Determine its equation.

Q. If a curve passes through the point

(1, 0)

and has slope

(1 + \frac{1}{x^{2}})

at any point (x, y) on it, then the ordinate of point on the curve whose abscissa is

- 3

, is?

Q. The normal at any point

P (x, y)

of a curve meets the x-axis at

Q

and

N

is the foot of the ordinate at

P

.
If

N Q = \frac{x (1 + y^{2})}{1 + x^{2}},

then equation of such curve, given that it passes through the point

(3, 1)

is:

Find the equation of a curve passing through the point (0,-2) given that at any point (x, y)on the curve the product of the slope of its tangent and y co-ordinate of the point is equal to the x co-ordinate of the point.

Join BYJU'S Learning Program