SATHEE: Straight Line and Pair of Straight Lines 2 Question 6

Straight Line and Pair of Straight Lines 2 Question 6

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

(2005)

Show Answer

Answer:

Correct Answer: 6. $2 x = \pm (y - 1)$

Solution:

Here, the triangle formed by a line parallel to $X$ -axis passing through $P (h, k)$ and the straight line $y = x$ and $y = 2 - x$ could be as shown below:

Since, area of $△ A B C = 4 h^{2}$

$∴ \frac{1}{2} A B \cdot A C = 4 h^{2}$

where, $A B = \sqrt{2} | k - 1 |$ and $A C = \sqrt{2} (| k - 1 |)$

$\begin{aligned} \Rightarrow & \frac{1}{2} \cdot 2 (k - 1)^{2} & = 4 h^{2} \\ \Rightarrow & 4 h^{2} & = (k - 1)^{2} \\ \Rightarrow & 2 h & = \pm (k - 1) \end{aligned}$

The locus of a point is $2 x = \pm (y - 1)$ .

Straight Line and Pair of Straight Lines 2 Question 6

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Straight Line and Pair of Straight Lines 2 Question 6

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

Answer:

Engineering Preparation

Medical Preparation

NCERT Books & Solutions

Important Resources

Other Resources

Syllabus

Test Platform

Sample Mock Test

Mentorship

NCERT Exercise Video Solution

Menu

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