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Free CBSE - Class 11 Mathematics - Straight Lines worksheets

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1.
If sum of the perpendicular distances of a variable point P ($x$, $y$) from the lines $x + y – 5 = 0$ and $3x – 2y +7 = 0$ is always 10. Show that P must move on a line.
2.
Find equation of the line which is equidistant from parallel lines $9x + 6y – 7 = 0$ and $3x + 2y + 6 = 0$.
3.
A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the reflected ray passes through the point (5, 3). Find the coordinates of A.
4.
Prove that the product of the lengths of the perpendiculars drawn from the points ($\sqrt{a^2 - b^2}, 0$) and ($-\sqrt{a^2 - b^2}, 0$) to the line $\frac{x}{a} \cos\theta + \frac{y}{b} \sin\theta = 1$ is $b^2$.
5.
A person standing at the junction (crossing) of two straight paths represented by the equations $2x – 3y + 4 = 0$ and $3x + 4y – 5 = 0$ wants to reach the path whose equation is $6x – 7y + 8 = 0$ in the least time. Find equation of the path that he should follow.
6.
Find the distance between parallel lines (i) $15x + 8y – 34 = 0$ and $15x + 8y + 31 = 0$
7.
Find equation of the line perpendicular to the line $x – 7y + 5 = 0$ and having x intercept 3.
8.
The hypotenuse of a right angled triangle has its ends at the points (1, 3) and (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle which are parallel to the axes.
9.
Find the image of the point (3, 8) with respect to the line $x +3y = 7$ assuming the line to be a plane mirror.
10.
If the lines $y = 3x +1$ and $2y = x + 3$ are equally inclined to the line $y = mx + 4$, find the value of $m$.
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