Question

Problem 3. 3.3) The ellipse with center (0,0) and vertex (0,5) contains the point (2, V15). Write the canonical equation of the ellipse. Problem 4. (3.4] A hyperbola is given by the equation 16y2 - 92 = 144. Find the coordinates of vertices and foci, and the equations of the asymptotes.

Answer 1

Center (0,0) anel verten (0,5) . point (2,815) We know the staneland forms of Ellipse, centand cat corgina 02 be We know vertine = (BHb) = (0,5). bots M2 + y2 2. =1 Now let's use the point (2,515). 4 + 12 = 1 4 2 = 1 - 1 - 4 = 10 - q² = 100 - a= + 510 Bo equesion of Ellipse constant at Coio) is given by x² + y2 = 1 To 25 ans

164²_ qn2 sluu ame we know (Gorchenmates cef vertices are (0, 2b) so vertices coor dimecres (0,23) foci is given by (0,I() When c- Sartha - cats [foci= (0,25) een of asymptores are given log - y = + 9% (2-h+k and (21k) = (0,0) = centor. 18 = = 42 so