A line is drawn from a point P(x, y) on curve y = f(x), making an angle in anti-clockwise with the +ve x-axis which is supplementary to the one made by the tangent to the curve at P(x, y). The line meets the x-axis at A. Another line perpendicular to the first, is drawn from P(x, y) meeting the y-axis at B. If OA = OB, where O is the origin, then the curve which passes through (1, 1).
A line is drawn from a point P(x, y) on curve y = f(x), making an angle in anti-clockwise with the +ve x-axis which is supplementary to the one made by the tangent to the curve at P(x, y). The line meets the x-axis at A. Another line perpendicular to the first, is drawn from P(x, y) meeting the y-axis at B. If OA = OB, where O is the origin, then the curve which passes through (1, 1).
Option 1 -
x2 – y2 + 4xy = 4
Option 2 -
x2 – y2 – 2xy + 2 = 0
Option 3 -
x2 – y2 + 2xy = 2
Option 4 -
x2 – y2 – 4xy + 4 = 0
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1 Answer
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Correct Option - 3
Detailed Solution:The equation of the line through P (x, y) making an angle with the x-axis which is supplementary to the angle made by the tangent at P (x, y) is
At the point where it meets the x-axis
Y = 0, X = x
The line through P (x, y) and perpendicular to (1) is
At the point where it meets the y-axis
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