Calculation:The equation of parabola is y2 = 4kx ------(1)Let O be the vertex, S be the focus, and LL' be the latus rectum of the parabola.The equation of latus rectum is x = k.Also, here the parabola is symmetric about x?axis.Required area, A = 2(area of OSL)? Required area, A = 2 \(\displaystyle \int_0^ky\ dx\)? A = 2 \(\displaystyle \int_0^k2? k\ ? x\ dx\)? A = 2.2?k \(\displaystyle \int_0^k \ x^{\frac{1}{2}} dx\)? A = 4?k \(\displaystyle \ \left [ \frac{x^{\frac{3}{2}}}{\frac{3}{2}}\right]_0^k \)? A = \(\displaystyle \frac{8}{3}\ \sqrt k\ [k^\frac{3}{2}-0^\frac{3}{2}]\)? A = \(\displaystyle \frac{8}{3}\ k^2\)Since the area of the given parabola is 24.? 24 = \(\displaystyle \frac{8}{3}\ k^2\)? k = ± 3As the value of k > 0, k = 3.? The value of k = 3.