| Class XI |
Mathematics |
Mathematics |
9 |
to x-axis, or coincidingwithx-axis,haveinclinationof0°.The inclination of a vertical line (parallel to or coincidingwith y-axis)is90°. Definition 1... |
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| Class XI |
Mathematics |
Mathematics |
9 |
tan ( 180° – ∠ MPQ) = – tan ∠ MPQ MQ y2− y 1 y2− y1 . = − = − = x −x MP x1−x 2 2 1 Consequently, we see that in both the cases the slope m of the l... |
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| Class XI |
Mathematics |
Mathematics |
9 |
1 2 Hence, two non-vertical lines are perpendicular to each other if and only if their slopes are negative reciprocals of each other, i.e., m 2 − o... |
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| Class XI |
Mathematics |
Mathematics |
9 |
an1 L (Fig29.6). Then θ = α 2 α an1 α , α 1 902. Therefore tan θ = tan (α – α ) = tan α2 −tan α 1 = m 2m 1 (as 1 + m m ≠ 0) 2 1 1 +an α tanα 1 + m ... |
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| Class XI |
Mathematics |
Mathematics |
9 |
or 1= 2 , 4 1 1 1+ 2 1+ 2 1 1 m − 2 m − 2 =1 or = –1. whichgives 1+ 1 m 1+ 1 m 2 2 Reprint 2026-27 158 MATHEMATICS Therefore m =3 or m = − . 3 Henc... |
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| Class XI |
Mathematics |
Mathematics |
9 |
points (4, 4), (3, 5) and (–1, –1) are the vertices of a right angled triangle. ° 7. Findtheslopeoftheline,whichmakesanangleof30 withthepositivedir... |
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| Class XI |
Mathematics |
Mathematics |
9 |
9.8(b)]. Reprint 2026-27 160 MATHEMATICS Fig 9.8 Example 4 Find the equations of the lines parallel to axes and passing through (– 2, 3). Solution ... |
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| Class XI |
Mathematics |
Mathematics |
9 |
slope of P P = slope of P P 1 1 2 y − y y − y y − y i.e., 1= 2 1, or y − y1= 2 1( x− x 1). x− x1 x2− x1 x2 − x1 Thus, equation of the line passing ... |
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| Class XI |
Mathematics |
Mathematics |
9 |
L with slope m makes x-intercept d. Then equation of L is y = m(x – d) ... (4) Students may derive this equation themselves by the same method as i... |
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| Class XI |
Mathematics |
Mathematics |
9 |
or general equation of a line. EXERCISE9.2 In Exercises 1 to 8, find the equation of the line which satisfy the given conditions: 1. Write the equa... |
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| Class XI |
Mathematics |
Mathematics |
9 |
milk store finds that, he can sell 980 litres of milk each week at Rs 14/litre and 1220 litres of milk each week at Rs 16/litre. Assuming a linear ... |
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| Class XI |
Mathematics |
Mathematics |
9 |
C 2 C 2 C 2 2 QR = 0+ + ( − 0 ) = A +B A B AB Substituting the values of area (∆PQR) and QR in (1), we get Ax1+B y +C PM = 1 A2 +B 2 Reprint... |
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| Class XI |
Mathematics |
Mathematics |
9 |
By + C = 0, we get A = 3, B = – 4 and C = – 26. Given point is (x , y ) = (3, –5). The distance of the given point from given line is 1 1 3.3+ ( )(... |
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| Class XI |
Mathematics |
Mathematics |
9 |
angle. Find the value of h. Reprint 2026-27 168 MATHEMATICS 10. Provethatthelinethroughthepoint(x ,y )1nd1aralleltothelineAx+By+C=0is A (x –x 1 + B... |
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| Class XI |
Mathematics |
Mathematics |
9 |
lines is (1, 1). Since above three lines are concurrent, the point (1, 1) will satisfy equation (2) so that 5.1 + k .1 – 3 = 0 or k = – 2. Reprint ... |
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| Class XI |
Mathematics |
Mathematics |
9 |
x −3y +4 =0 , k −2 −1 so that = or 3h+ k =5 ... (2) h −1 1 h +1 k + 2 andthemid-pointofPQ,i.e., point , willsatisfytheequation(1)sothat 2 2... |
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| Class XI |
Mathematics |
Mathematics |
9 |
2 1 ( c2− c1) = 0 −c 2 + (c2−c +1) 0 c1− = 2 m 1m 2 m 1m 2 m 1m 2 2 m 1 − m 2 Example 15 A line is such that its segment between th... |
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| Class XI |
Mathematics |
Mathematics |
9 |
of a moving point such that its distances from two lines 3x – 2y = 5 and 3x + 2y = 5 are equal is a straight line. Solution Given lines are 3x – 2y... |
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| Class XI |
Mathematics |
Mathematics |
9 |
it meets the y-axis. 7. Find the area of the triangle formed by the lines y – x = 0, x + y = 0 and x – k = 0. 8. Find the value of p so that the th... |
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| Class XI |
Mathematics |
Mathematics |
9 |
the triangle which are parallel to the axes. 17. Find the image of the point (3, 8) with respect to the line x +3y = 7 assuming the line to be a pl... |
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| Class XI |
Mathematics |
Mathematics |
9 |
tan α, α ≠ 90°. Slopeofhorizontallineiszeroandslopeofverticallineisundefined. fi fi An acute angle (say θ) between lines L and1L with 2lopes m and m ... |
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| Class XI |
Mathematics |
Mathematics |
9 |
0 from a poi1t 1x , y ) Ax1+ B y1+C is given by d = 2 2 . A + B fi Distance between the parallel linesAx + By + 1 = 0 andAx + By + C 2 0, C1− C 2 is... |
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| Class XII |
Computer Science |
Computer Science |
6 |
Element 34 16 2 93 80 77 51 Hash Value 34%10=4 16%10=6 2%10=2 93%10=3 80%10=0 77%10=7 51%10=1 After computing the hash values, each element is inse... |
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| Class XII |
Accountancy |
Accountancy Part-II |
6 |
capital 7,00,000 5,00,000 b) Reserve and surplus 4,70,000 2,50,000 2. Non-current Liabilities (8% Debentures) 4,00,000 6,00,000 3. Current Liabilit... |
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| Class XII |
Accountancy |
Computerised Accounting System |
2 |
the merged cell, click Merge and Centre. The contents of the merged cell will appear in the upper-left cell of the range of split cells. • Formatti... |
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