If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie o...
If the points (-1, t -1), (t, t - 3) and (t - 6, 3) lie on the same straight line, find the values of t.
t = -2 and 3
t = 2 and -3
t = 2 and 3
t = -2 and -3
Correct answer is C
For collinear points (points on the same line), the slopes are equal for any 2 points on the line.
Given (-1, t - 1), (t, t - 3), (t - 6, 3),
slope=(t−3)−(t−1)t−(−1)=3−(t−3)(t−6)−t=3−(t−1)(t−6)−(−1)
Taking any two of the equations above, solve for t.
t−3−t+1t+1=6−t−6
12=(6−t)(t+1)
−t2+5t+6−12=0⟹t2−5t+6=0
Solving, we have t = 2 and 3.
Solve \log_{2}(12x - 10) = 1 + \log_{2}(4x + 3)...
Find the locus of points which is equidistant from P(4, 5) and Q(-6, -1). ...
The function f: x \to \sqrt{4 - 2x} is defined on the set of real numbers R. Find the domain of ...
A binary operation \Delta is defined on the set of real numbers, R, by \(a \Delta b = \frac{a+b}...
If ^nC_2 = 15, find the value of n...
If √5 cosx + √15sinx = 0, for 0° < x < 360°, find the values of x. ...
Given that \frac{1}{x^2 - 4} = \frac{p}{(x + 2)} + \frac{Q}{(x - 2}) x \neq \pm 2 Find the...