show that if the normals at the points P(at 1 ,2at 1 ) and G(at 2 2 ,2at 2 ) to the parabola y 2 =4ax, intersect on the paarabola, then t 1 t 2 = 2.

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Arun · Answer

Let the normals at P and Q meet at R(at 2 , 2at). Then t = – t 1 – 2/t 1 and t = – t 2 – 2/t 2 . Therefore t 1 + 2/t 1 = t 2 + 2/t 2 ⇒ (t 1 – t 2 ) = 2(t 1 -t 2 )/(t 1 t 2 ) ⇒ t 1 t 2 = 2.

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show that if the normals at the points P(at 1 ,2at 1 ) and G(at 2 2 ,2at 2 ) to the parabola y 2 =4ax, intersect on the paarabola, then t 1 t 2 = 2.

show that if the normals at the points P(at₁ ,2at₁ ) and G(at²₂ ,2at₂ ) to the parabola y² =4ax, intersect on the paarabola, then t₁t₂ = 2.

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show that if the normals at the points P(at 1 ,2at 1 ) and G(at 2 2 ,2at 2 ) to the parabola y 2 =4ax, intersect on the paarabola, then t 1 t 2 = 2.

show that if the normals at the points P(at1 ,2at1 ) and G(at22 ,2at2 ) to the parabola y2 =4ax, intersect on the paarabola, then t1t2 = 2.

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show that if the normals at the points P(at₁ ,2at₁ ) and G(at²₂ ,2at₂ ) to the parabola y² =4ax, intersect on the paarabola, then t₁t₂ = 2.