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# The number of normals to the parabola y2=8x through (2,1) is?

kkbisht
90 Points
2 years ago
Only one real normal can be drwan from the point (2,1)  to the parabola y^2=8x as the cubic equation formed from the equation of a normal to the parabola  has one real root and other two imaginari roots as follows:
Equation of normal: y=mx-2am-am3(slope form) and y+tx=2at+at^3 (parametric form with ‘t’ as parameter) Now this normal passes through (2,1) implies 1+2t=4t=2t^3 ( a=2 for the parabola y^2=8x) This equation has only one real value of ‘t’.You can easily find the roots of this cubic equation which has only one real root and other two root are imaginary