Question

Find the equation of ellipse having axes along the coordinate axes and passes through the points (4,3) and (-1,4)

Answer 1

As axes lie along coordinate axes, hence equation of ellipse will be:x2a2+y2b2=1 Ellipse passes through 4,3⇒42a2+32b2=1⇒16a2+9b2=1 ...iEllipse passes through -3,4⇒-32a2+42b2=1⇒9a2+16b2 =1 ....iii×9-ii×16144a2+81b2-144a2-256b=9-16⇒81-256b2=-7⇒-175b2=-7⇒b2=1757⇒b2=25Put value of b in ii9a2+1625 =1⇒9a2=1-1625⇒9a2=25-1625⇒9a2=925⇒1a2=125⇒a2=25Hence x2a2+y2b2=1 becomes:x225+y225=1