Distance Between Two Points Formula - Practice Questions & MCQ

The locus of the centres of the circles, which touch the circle,

$x^{2}+y^{2}=1$ externally , also touch the y-axis and lie in the

first quadrant, is :

The intersection of three lines $x-y=0,x+2y=3 \; \text {and} \; 2x+y=6$ is a :

A triangle with vertices $(4, 0), (–1, –1), (3, 5)$ is

If in a cartesian coordinate system Point A = (3,5) and point B = (5,7) find the distance between A and B ? 

If the distance between the points $(a, 0,1)$ and $(0,1,2)$ is $\sqrt{27}$, then the value of a is

If $P(\sqrt{2} \sec \theta, \sqrt{2} \tan \theta)$ is a point on the hyperbola whose distance from the origin is $\sqrt{6}$ (where P is in the first quadrant) then $\theta$ equals

The ratio in which the line 3x + 4y + 2 = 0 divides the distance between the lines 3x + 4y + 5 = 0 and 3x + 4y – 5 = 0 is

 

The value of 'a' if the distance between P(a, 5) and Q(2, a) is 7 units, is

Let the range of the function

$
f(x)=6+16 \cos x. \cos \left(\frac{\pi}{3}-x\right) . \cos \left(\frac{\pi}{3}+x\right)
$

$\sin 3 x. \cos 6 x, x \in R$ be $[\alpha, \beta]$. Then the distance of the point $(\alpha, \beta)$ from the line $3 x+4 y+12=0$ is: