The number of tangents to the parabola y^2=8x through (2,1) is
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Zero.
No tangent to y^2=8x at any point P(x1,y1) passes through Q(2,1). As P is between x axis and parabola.
Proof:
Slope of tangent at P: dy/dx= 4/y1
Slope of PQ = (y1-1)/(x1-2) = (y1-1)/(y1^2 /8 - 2) = 4/y1
=> y1^2 - 2 y1 + 16 = 0
No solutions to this quadratic.
No tangent to y^2=8x at any point P(x1,y1) passes through Q(2,1). As P is between x axis and parabola.
Proof:
Slope of tangent at P: dy/dx= 4/y1
Slope of PQ = (y1-1)/(x1-2) = (y1-1)/(y1^2 /8 - 2) = 4/y1
=> y1^2 - 2 y1 + 16 = 0
No solutions to this quadratic.
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