Q. 8 B5.0( 1 Vote )

# Find the condition for the following set of curves to interest orthogonally.

and

Answer :

Given:

Curves 1 ...(1)

& 1 ...(2)

First curve is 1

Differentiating above w.r.t x,

⇒ . = 0

⇒ .

⇒

⇒

⇒ m_{1} ...(3)

Second curve is 1

Differentiating above w.r.t x,

⇒ . = 0

⇒ .

⇒

⇒

⇒ m_{1} ...(4)

When m_{1} & m_{2} =

Since ,two curves intersect orthogonally,

⇒ × = – 1

⇒ × = – 1

⇒ ...(5)

Now equation (1) – (2) gives

⇒ x^{2}() – y^{2}() = 0

⇒ x^{2}() = y^{2}()

⇒

⇒

⇒

Substituting from equation (5),we get

⇒

⇒ – 1

⇒ ( – 1)(A^{2} – a^{2}) = (B^{2} – b^{2})

⇒ a^{2} – A^{2} = B^{2} – b^{2}

⇒ a^{2} + b^{2} = B^{2} + A^{2}

Rate this question :

Find the equation of all lines having slope 2 which are tangents to the curve

NCERT - Mathematics Part-IFind the equation of the normal to curve x2 = 4y which passes through the point (1, 2).

NCERT - Mathematics Part-IFind the equations of the tangent and normal to the given curves at the indicated points:

y = x^{3} at (1, 1)

Show that the normal at any point θ to the curve

x = a cosθ + a θ sinθ, y = a sinθ – aθ cosθ is at a constant distance from the origin.

NCERT - Mathematics Part-IFind the slope of the normal to the curve x = 1− a sinθ, y = bcos^{2} θ at

The slope of the tangent to the curve x = t^{2} + 3t – 8, y = 2t^{2} – 2t – 5 at the point (2,– 1) is

Find the equation of the normal at the point (am^{2}, am^{3}) for the curve ay^{2} = x^{3}.

Find the points on the curve x^{2} + y^{2} – 2x – 3 = 0 at which the tangents are parallel to the x-axis.

Find the equations of the tangent and normal to the given curves at the indicated points:

y = x^{2} at (0, 0)

The slope of the normal to the curve y = 2x^{2} + 3 sin x at x = 0 is