For any curve C (which is not a straight line), the distance of tangent at any point P on the curve C from origin, is equal to ordinate of point P. The curve passes through (1,1). Minimum distance of the point (0,5) from the curve C, is

Question

For any curve C (which is not a straight line), the distance of tangent at any point P on the curve C from origin, is equal to ordinate of point P. The curve passes through (1,1). Minimum distance of the point (0,5) from the curve C, is (A) 1 (B) 2 (C) 3 (D) 4

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/325b5fcc779a97ba6b22e8284b9520df-.png" /> ( dy / dx )=((2 xy / x 2- y 2)) ∴ On solving we get x2+(y-1)2=1 .

Q. For any curve $C$ (which is not a straight line), the distance of tangent at any point $P$ on the curve $C$ from origin, is equal to ordinate of point $P$ . The curve passes through $(1, 1)$ .
Minimum distance of the point $(0, 5)$ from the curve C, is

1

2

3

4

$\frac{d y}{d x} = (\frac{2 x y}{x ^{2} - y ^{2}})$
$∴$ On solving we get
$x^{2} + (y - 1)^{2} = 1.$

Q. For any curve C (which is not a straight line), the distance of tangent at any point P on the curve C from origin, is equal to ordinate of point P. The curve passes through (1,1). Minimum distance of the point (0,5) from the curve C, is

1

2

3

4

dxdy​=(x2−y22xy​) ∴ On solving we get x2+(y−1)2=1.

Q. For any curve $C$ (which is not a straight line), the distance of tangent at any point $P$ on the curve $C$ from origin, is equal to ordinate of point $P$ . The curve passes through $(1, 1)$ .
Minimum distance of the point $(0, 5)$ from the curve C, is

$\frac{d y}{d x} = (\frac{2 x y}{x ^{2} - y ^{2}})$
$∴$ On solving we get
$x^{2} + (y - 1)^{2} = 1.$