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Implicit Differentiation

lf a sin θ +...

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lf a sin θ + b cos θ = c, then prove that a cos θ -b sin θ =\sqrt{a^2+b^2-c^{

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Q. Question 11
If

a s i n θ + b c o s θ = c

, then prove that

a c o s θ - b s i n θ = \sqrt{a^{2} + b^{2} - c^{2}}

a c o s θ + b s i n θ = c

a c o s^{2} θ + 2 a s i n θ c o s θ + b s i n^{2} θ = c

where a,b,c, are all unequal quantities, then eliminate

θ

cos θ - sin θ = m

sec θ - cos θ = n

θ

cos θ - sin θ = a^{3}

a^{2} b^{2} (a^{2} + b^{2}) = 1

Q. Find the radius of a circle

(x c o s θ + y s i n θ - a)^{2} + (x s i n θ + y c o s θ - b)^{2} = k^{2}

θ

varies then prove that locus of the centre of above circle is again a circle.

Q. If x = a (cos θ + θ sin θ), y = a(sin θ − θ cos θ), prove that

\frac{d^{2} y}{d x^{2}} = \frac{\sec^{3} θ}{a θ}

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