If \(x = 2at^2\) and \(y = at^4\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = t^2\).
If \(x = a\cos\theta\) and \(y = b\cos\theta\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = \dfrac{b}{a}\).
If \(x = \sin t\) and \(y = \cos 2t\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = -4\sin t\).
If \(x = 4t\) and \(y = \dfrac{4}{t}\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = -\dfrac{1}{t^2}\).
If \(x = \cos\theta - \cos 2\theta\) and \(y = \sin\theta - \sin 2\theta\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = \dfrac{\cos\theta - 2\cos 2\theta}{2\sin 2\theta - \sin\theta}\).
If \(x = a(\theta - \sin\theta)\) and \(y = a(1 + \cos\theta)\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = -\cot\left(\dfrac{\theta}{2}\right)\).
If \(x = \dfrac{\sin^3 t}{\sqrt{\cos 2t}}\) and \(y = \dfrac{\cos^3 t}{\sqrt{\cos 2t}}\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = -\cot 3t\).
If \(x = a\left(\cos t + \log\tan\dfrac{t}{2}\right)\) and \(y = a\sin t\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = \tan t\).
If \(x = a\sec\theta\) and \(y = b\tan\theta\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = \dfrac{b}{a}\cosec\theta\).
If \(x = a(\cos\theta + \theta\sin\theta)\) and \(y = a(\sin\theta - \theta\cos\theta)\), find \(\dfrac{dy}{dx}\) without eliminating the parameter.
\(\dfrac{dy}{dx} = \tan\theta\).
If \(x = \sqrt{a^{\sin^{-1} t}}\) and \(y = \sqrt{a^{\cos^{-1} t}}\), show that \(\dfrac{dy}{dx} = -\dfrac{y}{x}\).
\(\dfrac{dy}{dx} = -\dfrac{y}{x}\).