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Visual Solutions

10 step-by-step animated solutions for Straight Lines. Each solution breaks the problem into visual clips with key insights.

PYQ 2024 · Jan Shift 1Standard4 steps
The portion of the line 4x+5y=204x + 5y = 20 in the first quadrant is trisected by the lines L1L_1 and L2L_2 passing through the origin. The tangent of the angle between the lines L1L_1 and L2L_2 is:
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PYQ 2024 · Jan Shift 2Tricky4 steps
Let R be the interior region between the lines 3x−y+1=03x - y + 1 = 0 and x+2y−5=0x + 2y - 5 = 0 containing the origin. The set of all values of aa, for which the points (a2,a+1)(a^2, a+1) lie in RR, is:
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PYQ 2024 · Jan Shift 2Standard4 steps
Let A and B be two finite sets with m and n elements respectively. The total number of subsets of A is 56 more than the total number of subsets of B. Then the distance of the point P(m,n)P(m, n) from the point Q(−2,−3)Q(-2, -3) is:
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PYQ 2024 · Jan Shift 1Standard4 steps
A line passing through the point A(9,0)A(9, 0) makes an angle of 30°30° with the positive direction of the x-axis. If this line is rotated about A through an angle of 15°15° in the clockwise direction, then its equation in the new position is:
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PYQ 2024 · Jan Shift 2Standard4 steps
Let A be the point of intersection of the lines 3x+2y=143x + 2y = 14, 5x−y=65x - y = 6 and B be the point of intersection of the lines 4x+3y=84x + 3y = 8, 6x+y=56x + y = 5. The distance of the point P(5,−2)P(5, -2) from the line AB is:
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PYQ 2024 · Jan Shift 1Tricky4 steps
In a △ABC\triangle ABC, suppose y=xy = x is the equation of the bisector of angle B and the equation of the side AC is 2x−y=22x - y = 2. If 2AB=BC2AB = BC and the point A and B are respectively (4,6)(4, 6) and (α,β)(\alpha, \beta), then α+2β\alpha + 2\beta is equal to:
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PYQ 2024 · Jan Shift 2Tricky4 steps
If the sum of squares of all real values of α\alpha, for which the lines 2x−y+3=02x - y + 3 = 0, 6x+3y+1=06x + 3y + 1 = 0 and αx+2y−2=0\alpha x + 2y - 2 = 0 do not form a triangle, is pp, then the greatest integer less than or equal to pp is:
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PYQ 2024 · Jan Shift 2Tricky4 steps
The distance of the point (2,3)(2, 3) from the line 2x−3y+28=02x - 3y + 28 = 0, measured parallel to the line 3x−y+1=0\sqrt{3}x - y + 1 = 0, is equal to:
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PYQ 2024 · Apr Shift 2Standard4 steps
Let A(−1,1)A(-1, 1) and B(2,3)B(2, 3) be two points and PP be a variable point above the line ABAB such that the area of △PAB\triangle PAB is 10. If the locus of PP is ax+by=15ax + by = 15, then 5a+2b5a + 2b is:
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PYQ 2024 · Apr Shift 1Tricky4 steps
A ray of light coming from the point P(1,2)P(1, 2) gets reflected from the point QQ on the x-axis and then passes through the point R(4,3)R(4, 3). If the point S(h,k)S(h, k) is such that PQRSPQRS is a parallelogram, then hk2hk^2 is equal to:
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