Coordinate Geometry - Study Mode

[#86] The equation of circle with centre (1, -2) and radius 4 cm is:
Correct Answer

(D) x 2 + y 2 - 2x + 4y = 11

Explanation

Solution: (x - a) 2 + (y - b) 2 = r 2 (x - 1) 2 + [y - (-2)] 2 = 4 2 x 2 - 1 - 2x + y 2 + 4 + 4y = 16 x 2 + y 2 - 2x + 4y = 11

[#87] An equation of the form ax + by + c = 0 where a ≠ 0, b ≠ 0, c = 0 represents a straight line which passes through:
Correct Answer

(A) (0, 0)

Explanation

Solution: ax + by + c = 0 Where c = 0, a ≠ 0 & b ≠ 0 ∴ ax + by = 0 Since ax + by = 0, therefore x = 0 & y = 0 Therefore, the straight line passes through (0, 0)

[#88] What is the area (in unit squares) of the region enclosed by the graphs of the equations 2x - 3y + 6 = 0, 4x + y = 16 and y = 0?
Correct Answer

(A) 14

Explanation

Solution: 2x - 3y + 6 = 0 y = 0 ⇒ 2x - 3 × 0 = -6 2x = -6 x = -3 y = 0 y = 0 ⇒ 4x + 0 = 16 x = 4
y = 0 $$eqalign{
& 2x - 3y = - 6,,, * 2 cr
& underline {4x + y = 16,,} ,,,,, * 1 cr} $$ 4x - 6y = -12 . . . . . . (i) 4x + y = 16 . . . . . . (ii) Solve equation (i) and (ii) y = 4
x = 3 $$Delta { ext{ABC}} = frac{1}{2} imes left( {4 + 3}
ight) imes 4 = 14$$

[#89] 2x - ky + 7 = 0 and 6x - 12y + 15 = 0 has no solution for
Correct Answer

(C) k = 4

Explanation

Solution: $$eqalign{
& { ext{For no - solution,}} cr
& frac{{{a_1}}}{{{a_2}}} = frac{{{b_1}}}{{{b_2}}}
e frac{{{c_1}}}{{{c_2}}} cr
& 2x - ky + 7 = 0{ ext{ and }}6x - 12y + 15 = 0 cr
& herefore frac{2}{6} = frac{{ - k}}{{12}} cr
& k = 4 cr} $$

[#90] What is the area (in unit squares) of the triangle enclosed by the graphs of 2x + 5y = 12, x + y = 3 and the x-axis?
Correct Answer

(A) 3

Explanation

Solution: $$eqalign{
& 2x + 5y = 12 cr
& x{ ext{ - axis}}:y = 0,
,x = 6 cr
& x + y = 3 cr
& x{ ext{ - axis}}:y = 0,
,x = 3 cr
& 2x + 5y = 12,,,,,*1 cr
& underline {,x + y = 3,,,,,,,,,,,,*2,} cr
& ,,,,,2x + 5y = 12 cr
& ,,,,,2x + 2y = 6 cr
& underline {,, - ,,,,,, - ,,,,,,,, - ,,,,} cr
& ,,,,,3y = 6 cr
& ,,,,,,y = 2 cr
& ,,,,,,x = 3 - 2 = 1 cr} $$ $$eqalign{
& { ext{Area of traingle}} = frac{1}{2} imes { ext{base}} imes { ext{height}} cr
& = frac{1}{2} imes 3 imes 2 cr
& = 3 cr} $$