Question and Answers Forum

All Questions      Topic List

Coordinate Geometry Questions

Previous in All Question      Next in All Question      

Previous in Coordinate Geometry      Next in Coordinate Geometry      

Question Number 49526 by ajfour last updated on 07/Dec/18

Commented by ajfour last updated on 07/Dec/18

$$Ifboththecolouredareasareequal,$$$$findequationofparabolainterms$$$$ofellipseparameters\mathit{a}and\mathit{b}.$$

Answered by ajfour last updated on 07/Dec/18

$$y={Ax}^2-b,\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$$$\frac{x^2}{a^2}+\frac{{({Ax}^2-b)}^2}{b^2}=1$$$$A^2{x}^4+(\frac{b^2}{a^2}-2Ab)x^2=0$$$$\Rightarrow x_P=\frac{\sqrt{2Ab-\frac{b^2}{a^2}}}{A}$$$$\Rightarrow {\int }_0^{x_P}(b\sqrt{1-\frac{x^2}{a^2}}-{Ax}^2+b)dx=\frac{\pi ab}{4}.$$$$$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com