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find the length of a chord of parabola passing through the vertex and making an angle theta with the x-axis

find the length of a chord of parabola passing through the vertex and making an angle theta with the x-axis

Grade:

1 Answers

Aman Bansal
592 Points
8 years ago

Dear Sai,

Let F(h, k) be the focus and the equation ax + by + c = 0 be the equation of the directrix of a parabola. Let P(x, y) be any point on the parabola and let PM be the perpendicular drawn from p on the directrix .

Then PF = PM => √(x - h)2 + (y - k)= ax + by + c/√a+ b2

=> (x - h)2 + (y - k)= (ax + by + c)2/a2 + b2

=>a2 + b2)[(x - h)+ (y - k)2] = (ax + by + c)2

=> (bx - ay)2 + 2(-ha- hb2 - ac) x + 2( - ka- kb- bc)y + (h2a+ h2b+ k2a+ k2b- c2) = 0

This is of the form (bx - ay)+ 2gx + 2fy + d = 0.

Thus , the general form of parabola equation is a second degree equation in which second degree terms form a perfect square. Solve parabola equation in the above method. Also for more help one can connect to an online tutor and get the required help.

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Thanks

Aman Bansal

Askiitian Expert


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