If the equation of the ellipse whose axes are coincident with the coordinate axes and  which touches the straight lines 3x−2y−20=0 and x+6y−20=0 is x2a2+y2b2=1, then a+b=

Let the equation of the ellipse be x2a2+y2b2=1…………….(1)Equation of the tangent to the ellipse in slope form isy=mx±a2m2+b2……………2 Given equation of the tangent is 3x−2y−20=0Compare (2) and (3)⇒m=32 and a2m2+b2=100⇒a294+b2=100⇒9a2+4b2=400………⋯⋯4 Given equation of the another tangent is x+6y−20=0⇒y=−16x+103………………5Compare (2) and (5) We get m=−16 and a2m2+b2=1009⇒a236+b2=1009⇒a2+36b2=400……6Now solving equations (4) & (6)  we get a2=40 and b2=10⇒a=40=210,b=10⇒a+b=310Therefore, the correct answer is (3).