Question 1:Find the values of k for which the line (k–3) x – (4 – k2) y + k2 –7k + 6 = 0 is<br> (a) Parallel to the x-axis,<br> (b) Parallel to the y-axis,<br> (c) Passing through the origin.<br>
Question 2:Find the values of q and p, if the equation x cos q + y sinq = π is the normal form<br> of the line 3 x + y + 2 = 0.<br>
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Question 3:Find the equations of the lines, which cut-off intercepts on the axes whose sum<br> and product are 1 and – 6, respectively.<br>
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Question 4:What are the points on the y-axis whose distance from the line 1<br> 3 4<br> x y + = is<br> 4 units.<br>
Question 5:Find perpendicular distance from the origin to the line joining the points (cosq, sin q)<br> and (cos f, sin f).<br>
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Question 6:Find the equation of the line parallel to y-axis and drawn through the point of<br> intersection of the lines x – 7y + 5 = 0 and 3x + y = 0.<br>
Question 7:Find the equation of a line drawn perpendicular to the line 1<br> 4 6<br> + = x y<br> through the<br> point, where it meets the y-axis.<br>
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Question 8:Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0.<br>
Question 9:Find the value of π so that the three lines 3x + y – 2 = 0, px + 2 y – 3 = 0 and<br> 2x – y – 3 = 0 may intersect at one point.<br>
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Question 10:If three lines whose equations are y = m1x + c1, y = m2x + c2 and y = m3x + c3 are<br> concurrent, then show that m1(c2 – c3) + m2 (c3 – c1) + m3 (c1 – c2) = 0.<br>
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Question 11:Find the equation of the lines through the point (3, 2) which make an angle of 45o<br> with the line x – 2y = 3.<br>
Question 12:Find the equation of the line passing through the point of intersection of the lines<br> 4x + 7y – 3 = 0 and 2x – 3y + 1 = 0 that has equal intercepts on the axes.<br>
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Question 13:Show that the equation of the line passing through the origin and making an angle<br> q with the line y mx c is<br> y<br> x<br> m<br> m<br> = + =<br> ± tan ‚<br> 1m tan ‚ .<br>
Question 14:In what ratio, the line joining (–1, 1) and (5, 7) is divided by the line x + y = 4?<br>
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Question 15:Find the distance of the line 4x + 7y + 5 = 0 from the point (1, 2) along the line<br> 2x – y = 0.<br>
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Question 16:Find the direction in which a straight line must be drawn through the point (–1, 2)<br> so that its point of intersection with the line x + y = 4 may be at a distance of<br> 3 units from this point.<br>
Question 17:The hypotenuse of a right angled triangle has its ends at the points (1, 3) and<br> (– 4, 1). Find an equation of the legs (perpendicular sides) of the triangle.<br>
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Question 18:Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the<br> line to be a plane mirror.<br>
Question 19:If the lines y = 3x +1 and 2y = x + 3 are equally inclined to the line y = mx + 4, find<br> the value of m.<br>
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Question 20:If sum of the perpendicular distances of a variable point P (x, y) from the lines<br> x + y – 5 = 0 and 3x – 2y +7 = 0 is always 10. Show that P must move on a line.<br>
Question 21:Find equation of the line which is equidistant from parallel lines 9x + 6y – 7 = 0<br> and 3x + 2y + 6 = 0.<br>
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Question 22:A ray of light passing through the point (1, 2) reflects on the x-axis at point A and the<br> reflected ray passes through the point (5, 3). Find the coordinates of A.<br>
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Question 23:Prove that the product of the lengths of the perpendiculars drawn from the<br> points ( ) 2 2 a − b ,0 and ( 2 2 ) − a − b ,0 to the line<br> 2 cos sin 1is<br> x y<br> b<br> a b<br> + = .<br>
Question 24:A person standing at the junction (crossing) of two straight paths represented by<br> the equations 2x – 3y + 4 = 0 and 3x + 4y – 5 = 0 wants to reach the path whose<br> equation is 6x – 7y + 8 = 0 in the least time. Find equation of the path that he<br> should follow.
