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Q.

The orthocentric of the triangle formed by the lines xy+3x+3y+9=0 and the line 3x+4y−5=0 is

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a

3,3

b

-3,3

c

3,-3

d

-3,-3

answer is D.

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Detailed Solution

The given pair of lines is xy+3x+3y+9=0 The above equation represents x+3=0 and y+3=0 which are perpendicularThe triangle formed by the given lines is right angle triangle. So that the ortho center of the triangle is vertex at right angle. Hence the point of intersection of x+3=0and y+3=0 is ortho centerTherefore, the ortho center is −3,−3
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The orthocentric of the triangle formed by the lines xy+3x+3y+9=0 and the line 3x+4y−5=0 is