Question

Consider the equations 5y²=16x and y²=8x-24. What is the pointbof intersection of the given curves on the first quadrant?⁼

Answer 1

$\text{Given, two curves}\space 5y^2=16x \space and \space y^2=8x-24.\newline Let f_1:y=\sqrt{\frac{16x}{5}} and f_2:y=\sqrt{8x-5}.\newline \text{Point of interestion are those points where the given two graph equation have same value.}\newline \text{Intersecting points given by,} f_1=f_2\newline \sqrt{\frac{16x}{5}}=\sqrt{8x-5}\newline \frac{16x}{5}=8x-24\newline 16x=40x-120\newline x=5\newline Then, y=\sqrt{8×5-24}\newline =\pm4 \text{Therefore, point of interestion are }(5,-4)and(5,4).$