mathemerize

Diameter Form of Circle – Equation and Examples

Diameter Form of Circle Equation The equation of the circle drawn on the straight line joining two points \((x_1, y_1)\) and \((x_2, y_2)\) is (\(x-x_1\))(\(x-x_2\)) + (\(y-y_1\))(\(y-y_2\)) = 0. This is known as diameter form of circle. where \((x_1, y_1)\) and \((x_2, y_2)\) are coordinates of two ends of diameter of circle. Note – If …

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Equation of Normal to a Circle with Examples

The normal at a point is the straight line which is perpendicular to the tangent to circle at the point of contact. Normal at a point of the circle passes through the center of circle. Here, you will learn how to find equation of normal to a circle with example. Equation of Normal to a …

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Equation of Tangent to a Circle – Condition of Tangency

When a straight line meet a circle on two coincident points then it is called the tangent to a circle. Here, you will learn condition of line to be a tangent  to a circle and equation of tangent to a circle with example. Condition of Tangency : The line L = 0 touches the circle …

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How to Determine Odd Even Function

Here, you will learn what is odd even functions and how to determine if given function is odd or even with example. Let’s begin – Odd Even Function : Let a function f(x) such that both x and -x are in its domain then If f(-x) = f(x) then f is said to be an …

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Equation of Tangent to Parabola in all Forms

The equation of tangent to parabola in point form, slope form and parametric form are given below with examples. Condition of Tangency for Parabola : (a)  The line y = mx + c meets the parabola \(y^2\) = 4ax in two points real, coincident or imaginary according as a >=< cm \(\implies\) condition of tangency …

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Equation of Normal to Ellipse in all Forms

Equation of Normal to ellipse : \(x^2\over a^2\) + \(y^2\over b^2\) = 1 (a) Point form : The Equation of normal to the given ellipse at (\(x_1, y_1\)) is \(a^2x\over x_1\) + \(b^2y\over y_1\) = \(a^2-b^2\) = \(a^2e^2\) Example : Find the normal to the ellipse \(9x^2+16y^2\) = 288 at the point (4,3). Solution : …

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