Solution : Since, Slope of line passing through two points is m = \(y_2 – y_1\over x_2 – x_1\). so, slope of chord passing through two points is \(4-(-3)\over 3-2\) = 7 Now, Tangent line is parallel to chord. Therefore slope of tangent line is equal to slope of chord, Hence slope of tangent line …
The slope of tangent parallel to the chord joining the points (2, -3) and (3, 4) is Read More »
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 common tangent to the parabola \(y^2\) = 4ax and \(x^2\) = 4ay ? Read More »
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 equation of tangent to the parabola having slope m? Read More »
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 …
What is the number of parking space covered by the car? Read More »
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 …
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) …
Here you will learn what is the relation between roots and coefficients of quadratic equation with examples. Let’s begin – The general form of quadratic equation is \(ax^2 + bx + c\) = 0, a \(\ne\) 0. The root of the given equation can be found by using the formula : x = \(-b \pm \sqrt{b^2 …
Relation Between Roots and Coefficients of Quadratic Equation Read More »
Here you will learn how to find the nature of roots of quadratic equation using discriminant with examples. Let’s begin – Nature of Roots of Quadratic Equation (a) Consider the quadratic equation \(ax^2 + bx + c\) = 0 where a, b, c \(\in\) R & a \(\ne\) 0 , then x = \(-b \pm …
Here you will learn how to solve quadratic equation using quadratic formula or sridharacharya formula with examples. Let’s begin – Solve Quadratic Equation Using Quadratic Formula (Sridharacharya Formula) For the equation \(ax^2 + bx + c\) = 0, if \(b^2 – 4ac\) \(\ge\) 0, then x = (\(-b + \sqrt{b^2 -4ac}\over 2a\)) and x = …
Solve Quadratic Equation Using Quadratic Formula Read More »
Here, you will learn completion of square method and how to solve quadratic equation by completing the square with examples. Let’s begin – Solve Quadratic Equation by Completing the Square Let us consider the equation \(x^2 + 8x + 4\) = 0 If we want to factorize the left hand side of the equation using …
Solve Quadratic Equation by Completing the Square Read More »
