If the normal to the rectangular hyperbola xy=c2 at the point (ct,ct) meets the curve again at (ct′,ct′), then
A
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution
The correct option is B Equation of the tangent at (ct,ct) to the hyperbola xy=c2 is cxt+cty=2c2 Slope of the tangent =–1t2 and slope of the normal =t2 Equation of the normal at (ct,ct) is y−ct=t2(x–ct) If it passes through (ct′,ct), then ct′−ct=t2(ct′−ct)⇒(t–t′)=t3t′(t′–t)⇒t3t′=−1