The equation of a curve is Ax2+By2+Cy=8Ax^{2}+By^{2}+Cy=8, where AA, BB and CC are constants. The curve has a tangent parallel to the y-axis at the point (2,1). Given that dydx=32\dfrac{dy}{dx}=\dfrac{\sqrt{3}}{2} and d2ydx2=94\dfrac{d^{2}y}{dx^{2}}=\dfrac{9}{4} at the point where the curve cuts the positive x-axis, find the values of AA, BB and CC.

Implicit parametric中文
Work through it with AI →

It won't just hand you the answer — it asks where you're stuck.How the checker works

Worked solution

No solution to show yet.

Worked this one out on paper? Snap your steps and Gigle's AI math checker will circle the step where it went wrong.

More questions on this topic

  1. 1The curve C has equation x+y=(x−y)2x + y = (x - y)^2. It is given that C has only one turning point. Show that 1−dydx=21+2x−2y1 - \frac{dy}{dx} = \frac{2}{1 + 2x - 2y}…
  2. 2The curve C has equation x+y=(x−y)2.x + y = (x - y)^2. It is given that C has only one turning point. Show that 1−dydx=21+2x−2y1 - \dfrac{dy}{dx} = \dfrac{2}{1 + 2x - 2y}…
  3. 3A curve C1C_1 has the equation p2x2−y2=p2p^2x^2 - y^2 = p^2 where p>1p > 1. Sketch C1C_1, stating the coordinates of any points o…
  4. 4A curve CC has parametric equations x=2cos⁡θ+cos⁡2θ,y=2sin⁡θ−sin⁡2θ,x = 2\cos\theta + \cos 2\theta, \quad y = 2\sin\theta - \sin 2\theta, where 0<θ<2π0 < \theta < 2\pi…
  5. 5It is given that y=1+tan⁡−12xy = \sqrt{1 + \tan^{-1} 2x} where −12<x<12-\frac{1}{2} < x < \frac{1}{2}. Show that yd2ydx2+(dydx)2+8x(1+4x2)2=0.y \frac{\mathrm{d}^2 y}{\mathrm{d}x^2} + \left(\frac{\mathrm{d}y}{\mathrm{d}x}\right)^2 + \frac{8x}{(1 + 4x^2)^2} = 0.…