# Maths Questions

## What is the equation of common tangent to the parabola $$y^2$$ = 4ax and $$x^2$$ = 4ay ?

Solution : The equation of tangent in slope form to $$y^2$$ = 4ax is y = mx + $$a\over m$$ Now, if it is common to both parabola, it also lies on second parabola then $$x^2$$ = 4a(mx + $$a\over m$$) $$mx^2 – 4am^2 – 4a^2$$ = 0 has equal roots. then its discriminant is …

## What is the equation of tangent to the parabola having slope m?

Solution : The Equation of tangent to the parabola having slope ‘m’, is y = mx + $$a\over m$$ ,  (m $$\ne$$ 0) and point of contact  is ($$a\over m^2$$, $$2a\over m$$). Similar Questions The sum of the slopes of the tangent of the parabola $$y^2$$=4ax drawn from the point (2,3) is Find the locus …

## What is the number of parking space covered by the car?

Question : This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong for six-year-olds. Supposedly the students had just 20 seconds to solve the problem! Solution : Answer is 87. This is not a maths question, its just a tricky question. If you flip the …

## If the lines 3x-4y-7=0 and 2x-3y-5=0 are two diameters of a circle of area 49π square units, then what is the equation of the circle?

Solution : Area = 49π π$$r^2$$ = 49π r = 7 Now find the coordinates of center of circle by solving the given two equations of diameter. By solving the above equation through elimination method we get, x = 1 and y =-1 which are the coordinates of center of circle. Now the general equation …

## A coin is tossed successively three times. Find the probability of getting exactly one head or two heads.

Solution : We know that probability of event = no. of favorable outcome/total outcome Sample space of event : { (H , H , H) , (H , H , T) , (H , T , H) , (H , T , T) , (T , H , H) , (T , H , T) …