\(x^{2} + y^{2} - 4x - 6y - 12 = 0\)
\(x^{2} + y^{2} - 4x + 6y - 12 = 0\)
\(x^{2} + y^{2} + 4x + 6y - 12 = 0\)
\(x^{2} + y^{2} + 4x - 6y - 12 = 0\)
Correct answer is D
Equation of a circle with centre coordinates (a, b) : \((x - a)^{2} + (y - b)^{2} = r^{2}\)
Area of circle = \(\pi r^{2} = 25\pi cm^{2} \implies r^{2} = 25 \)
\(\therefore r = 5cm\)
(a, b) = (-2, 3)
Equation: \((x - (-2))^{2} + (y - 3)^{2} = 5^{2}\)
\(x^{2} + 4x + 4 + y^{2} - 6y + 9 = 25 \implies x^{2} + y^{2} + 4x - 6y + 13 - 25 = 0\)
= \(x^{2} + y^{2} + 4x - 6y - 12 = 0\)
-4
-1
3
4
Correct answer is C
\(y = 1 - 3x + 2x^{3}\)
\(\frac{\mathrm d y}{\mathrm d x} = -3 + 6x^{2}\)
At (1, 0), \(\frac{\mathrm d y}{\mathrm d x} = -3 + 6(1^{2}) = -3 + 6 = 3\)
\(y = mx - 3 \implies \frac{\mathrm d y}{\mathrm d x} = m = 3\) (Tangent with equal gradient)
-1
-2
-3
-4
Correct answer is D
\(x + 3 = 0 \implies x = -3\)
Using remainder theorem, if x + 3 is a factor, f(-3) = 0.
\(f(-3) = (-3)^{3} + 3(-3)^{2} + n(-3) - 12 = 0\)
\(-27 + 27 - 3n - 12 = 0 \implies -3n = 12\)
\(n = -4\)
x < -4 or x > 2
x < -2 or x > 4
-2 < x < 4
-4 < x < 2
Correct answer is B
No explanation has been provided for this answer.
What is the angle between \(a = (3i - 4j)\) and \(b = (6i + 4j)\)?
13°
87°
100°
110°
Correct answer is B
\(a . b = |a||b| \cos \theta\)
\(a = 3i - 4j; b = 6i + 4j\)
\(18 - 16 = (\sqrt{3^{2} + (-4)^{2}})(\sqrt{6^{2} + 4^{2}}) \cos \theta\)
\(2 = 5\sqrt{52} \cos \theta\)
\(\cos \theta = \frac{2}{5\sqrt{52}} = 0.0555\)
\(\theta = 86.8° \approxeq 87°\)