4x2+36y 2-4x+24y+1=0 at the point(1/2,-2/3) Find the equations of the tangents and normals to the ellipse Share with your friends Share 2 Neha Sethi answered this Dear student We have, 4x2+36y2-4x+24y+1=0⇒4x2-4x+1+36y2+24y+22=22⇒2x-12+6y+22=4⇒2x-1222+6y+2222=1⇒4(2x-1)22+126y+222dydx=0dydx=-2x-136y+2So, at the point 12,-23 ,dydx12,-23=-2×12-136×-23+2=0⇒dydx12,-23=0Thus, equation of the tangent at 12,-23 isy+23=0x-12⇒y+23=0⇒3y+2=0And equation of the normal at 12,-23 isy+23=0x-12⇒y+23=0⇒3y+2=0 Regards -4 View Full Answer
