27x2+16y 2-18x+8y-15=0 at the point(2/3,3/4)Find the equations of the tangents and normals to the ellipse. Share with your friends Share 0 Lovina Kansal answered this Dear student We have,27x2+16y2-18x+8y-15=0⇒33x2-18x+3+16y2+8y+1=11⇒33x-32+4y+12=11⇒33x-3211+4y+1211=1⇒6333x-311+84y+111dydx=0⇒dydx=-6333x-311×1184y+11⇒dydx=-6333x-38(4y+1)So, at the point 23.34,dydx23,34=-6333×23-384×34+1=-1832=-916⇒dydx23,34=-916Thus, equation of the tangent at 23,34 isy-34=-916x-23⇒4y-34=-9163x-23⇒16y-12=-9x+6⇒9x+16y-18=0And equation of the normal at 23,34 isy-34=169x-23⇒4y-34=1693x-23⇒108y-81=192x-128⇒192x-108y-47=0 Regards -1 View Full Answer
