(a) ay = bx (tan@)
(b) ay = bx (cot@)
(c) ay = by (tan@)
(d) None Of These
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Answer is the option (b). 4 x + 9 y = 18
Given Ellipse: E = 4 x² + 9 y² = 36 --- (1) .
Point P : (m , n) with m * n = m + n.
So m = n / (n-1) --- (2)
=> The only way m and n are both positive integers is if m = 2 & n = 2.
A tangent to Ellipse E at point A (x1, y1) is :
4 x1 * x + 9 y1 * y = 36 ---(3)
A tangent to Ellipse E at point B (x2, y2) is:
4 x2* x + 9 y2 * y = 36 ---(4)
The two tangents meet at P (m, n). So P lies on both tangents.
=> 4 m x1 + 9 n y1 = 36 , and
=> 4 m x2 + 9 n y2 = 36
From these eq. we find easily that line of joining A (x1,y1) & B(x2, y2) or the Chord of Contact (COC) is:
4 m x + 9 n y = 36
4 * 2 x + 9 * 2 y = 36 as m = 2 = n.
So 4x + 9 y = 18.
Answer..
Given Ellipse: E = 4 x² + 9 y² = 36 --- (1) .
Point P : (m , n) with m * n = m + n.
So m = n / (n-1) --- (2)
=> The only way m and n are both positive integers is if m = 2 & n = 2.
A tangent to Ellipse E at point A (x1, y1) is :
4 x1 * x + 9 y1 * y = 36 ---(3)
A tangent to Ellipse E at point B (x2, y2) is:
4 x2* x + 9 y2 * y = 36 ---(4)
The two tangents meet at P (m, n). So P lies on both tangents.
=> 4 m x1 + 9 n y1 = 36 , and
=> 4 m x2 + 9 n y2 = 36
From these eq. we find easily that line of joining A (x1,y1) & B(x2, y2) or the Chord of Contact (COC) is:
4 m x + 9 n y = 36
4 * 2 x + 9 * 2 y = 36 as m = 2 = n.
So 4x + 9 y = 18.
Answer..
kvnmurty:
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