I am given a point $P(2,3)$ thru which passing line forms triangle with axes of area $12$ , so how many lines will pass thru $P$ making same area with axes?

Writing intercept form of line

$$\frac{x}{a} + \frac{y}{b}=1$$ and then satisfying point in this equation I get $$2b+3a=ab$$ , now since area is $12$ hence $$1/2ab=12$$ we get $ab=24$ now substituting $ab$ and $b$ i get $$a^2 -8a +14=0$$ . Now we have 2 values for $a & b$ hence 2 lines should pass thru that points satisfying condition but correct answer is 3 , what I did wrong?


Of the three solutions, one triangle is in quadrant 1, one is in quadrant 2, and one is in quadrant 4.

You focused exclusively on a quadrant 1 triangle (from the assumption that $ab=24$. But you get solutions in the other quadrants if you look for solutions where $ab=-24$).

By the way for the first quadrant: From your equations $ab=24$ and $\frac2a+\frac3b=1$, you get $b=\frac{24}{a}$, which leads to $a^2-8a+16=0$. This quadratic has only one (double) root of $a=4$.


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.