Coordinate Geometry - Study Mode
[#71] A line cuts the x axis at the point (-3, 0) and the y-axis at the point (0, 6). What is the equation of the line?
Correct Answer
(D) y = 2x + 6
Explanation
Solution: [x08egin{array}{*{20}{c}}
{{ ext{Point }}left( { - 3,,0}
ight){ ext{ and }}left( {0,,6}
ight)} \
{,,,,,,,,,,,,,,,,,,{x_1}{y_1},,,,,,,,,,,,,,,,,,,{x_2}{y_2}}
end{array}] $$eqalign{
& { ext{Equation of line}} cr
& y - {y_1} = frac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}left( {x - {x_1}}
ight) cr
& y - 0 = frac{{6 - 0}}{{0 - left( { - 3}
ight)}}left( {x - left( { - 3}
ight)}
ight) cr
& y = frac{6}{3}left( {x + 3}
ight) cr
& y = 2x + 6 cr} $$
[#72] Find the coordinates of the points where the graph 57x - 19y = 399 cuts the coordinate axes.
Correct Answer
(C) x-axis at (7, 0) and y-axis at (0, -21)
[#73] The elimination of θ from xcosθ - ysinθ = 2 and xsinθ + ycosθ = 4 will give:
Correct Answer
(B) x 2 + y 2 = 20
Explanation
Solution: xcosθ - ysinθ = 2 . . . . . . (i) xsinθ + ycosθ = 4 . . . . . . (ii) Squaring equation (i) and equation (ii) and adding- x 2 + y 2 = 20
[#74] The graphs of the linear equations 3x - 2y = 8 and 4x + 3y = 5 intersect at the point P(α, β). What is the value of (2α - β)?
Correct Answer
(D) 5
Explanation
Solution: $$eqalign{
& 3{x_{ imes 3}} - 2{y_{ imes 3}} = {8_{ imes 2}} o left( { ext{i}}
ight) cr
& underline {4{x_{ imes 2}} + 3{y_{ imes 2}} = {5_{ imes 2}}} o left( {{ ext{ii}}}
ight) cr
& 17x = 34 cr
& x = 2 cr
& y = - 1 cr
& left( {2alpha - x08eta }
ight) = left{ {2left( 2
ight) - left( { - 1}
ight)}
ight} = 4 + 1 = 5 cr} $$
[#75] If (2 x )(2 y ) = 8 and (9 x )(3 y ) = 81, then (x, y) is:
Correct Answer
(A) (1, 2)
Explanation
Solution: 2 x . 2 y = 8 ⇒ 2 x + y = 2 3 On comparing both sides x + y = 3 . . . . . . . (i) Also, 9 x . 3 y = 81 ⇒ 3 2x . 3 y = 3 4 ⇒ 3 2x + y = 3 4 On comparing both sides 2x + y = 4 . . . . . . . (ii) On solving equation (i) and (ii) x = 1 y = 2 ∴ (x, y) = (1, 2)