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a straight line passing through the point P(1,2) and making an angle with the positive X axis 45 degree at the point Q and the value of PQ=3root2 then measure the coordinates of point Q |
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Answer» Answer: Step-by-step EXPLANATION: Method I The intersection point lies on circles with DIAMETER AB and AC SINCE there is right angle at the foot of the perpendicular. Equation of circle with diameter AB (x−4)(x−1)+(y+3)(y−1)=0 x2+y2–5x+2y+1=0(1) Equation of circle with diameter AC (x−4)(x−2)+(y+3)(y−3)=0 x2+y2–6x−1=0(2) Subtracting (2) from (1) we get equation of common chord AD which is perpendicular to BC x+2y+2=0 Method II Equation of BC (x2−x1)(y−y1)−(y2−y1)(x−x1) (2–1)(y−1)−(3–1)(x−1)=0 y−2x−1=0(3) equation of perpendicular is obtained by EXCHANGING the coefficients of x and y and changing sign of one of them.On R.H.S. put the values of point from which it passes. x+2y=4–6=−2 |
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