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Standard XII

Mathematics

Standard Equation of Parabola

The area of t...

Question

The area of the triangle formed by the intersection of a line parallel to $x$ -axis and passing through $P (h, k)$ with the lines $y = x$ and $x + y = 2$ is $4 h^{2}$ . Find the locus of the point $P$ .

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Solution

Area of triangle $= \frac{1}{2}$ . AB. AC $= 4 h^{2}$ and AB $= \sqrt{2} | k - 1 | =$ AC
$= ⟩ 4 h^{2} = \frac{1}{2} .2 . (k - 1)^{2}$
$= ⟩ k - l = \pm 2 h$ .
$= ⟩$ locus is $y = 2 x + 1, y = - 2 x + 1$ .

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The area of the triangle formed by the intersection of a line parallel to x-axis and passing through P(h,k) with the lines y=x and x+y=2 is 4h2. Find the locus of the point P.

Area of triangle =12. AB. AC =4h2 and AB =√2|k−1|= AC=⟩4h2=12.2. (k−1)2=⟩k−l=±2h.=⟩ locus is y=2x+1, y=−2x+1.

The area of the triangle formed by the intersection of a line parallel to $x$ -axis and passing through $P (h, k)$ with the lines $y = x$ and $x + y = 2$ is $4 h^{2}$ . Find the locus of the point $P$ .

Area of triangle $= \frac{1}{2}$ . AB. AC $= 4 h^{2}$ and AB $= \sqrt{2} | k - 1 | =$ AC
$= ⟩ 4 h^{2} = \frac{1}{2} .2 . (k - 1)^{2}$
$= ⟩ k - l = \pm 2 h$ .
$= ⟩$ locus is $y = 2 x + 1, y = - 2 x + 1$ .