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# Assertion :If the area of the triangle formed by the lines y=x,x+y=4 and the lines through P(h,k) parallel to y-axis is k2, then P lies on x2+y2−4x+4=0 Reason: Area of the triangle formed by the lines y=x,x+y=4 and the x-axis is equal to half the area of the triangle formed by the line x+y=4 and the coordinate axes.

A
Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
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B
Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
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C
Assertion is correct but Reason is incorrect
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D
Both Assertion and Reason are incorrect
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Solution

## The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for AssertionAssertionLet the third side be x=h, then the vertices are (2,2),(h,h) and (h,4−h)⇒k2=12∣∣ ∣∣221hh1h4−h1∣∣ ∣∣⇒2k2=∣∣ ∣∣221h−2h−20h−22−h0∣∣ ∣∣⇒k2+(h−2)2=0So, P(h,k) lies on x2+y2−4x+4=0Hence assertion is trueReason:Area of the first triangle is 4 and that of the second is 2.so it is true.  Suggest Corrections  0      Similar questions  Related Videos   Hyperbola and Terminologies
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