Here you will learn what is the formula for the length of latus rectum of ellipse with examples.. Let’s begin – Length of Latus Rectum of Ellipse (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b Length of the Latus Rectum = \(2b^2\over a\) Equation of latus rectum is x …
Here you will learn what is the formula to find the equation of directrix of ellipse with examples. Let’s begin – Directrix of Ellipse Equation (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b The equation of directrix is x = \(a\over e\) and x = \(-a\over e\) (ii) For …
Here you will learn what is the eccentricity of ellipse formula and how to find eccentricity with examples. Let’s begin – Eccentricity of Ellipse Formula (i) For the ellipse \(x^2\over a^2\) + \(y^2\over b^2\) = 1, a > b we have, \(b^2\) = \(a^2(1 – e^2)\) \(\implies\) \(e^2\) = 1 – \(b^2\over a^2\) \(\implies\) eccentricity …
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Here you will learn how to find the focus of parabola with examples. Let’s begin – Focus of Parabola Coordinates (i) For Parabola \(y^2\) = 4ax : The coordinates of focus is (a, 0). (ii) For Parabola \(y^2\) = -4ax : The coordinates of focus is (-a, 0). (iii) For Parabola \(x^2\) = 4ay : …
Here you will learn formula for finding the equation of directrix of parabola with examples. Let’s begin – Equation of Directrix of Parabola (i) For Parabola \(y^2\) = 4ax : The equation of directrix is x = -a. (ii) For Parabola \(y^2\) = -4ax : The equation of directrix is x = a. (iii) For …
Here you will learn formula to find the length of latus rectum of parabola with examples. Let’s begin – Latus Rectum of Parabola A double ordinate through the focus is called the latus rectum i.e. the latus rectum of a parabola is a chord passing through the focus perpendicular to the axis. In the given …
Here you will learn what is integration by substitution method class 12 with examples. Let’s begin – Integration By Substitution The method of evaluating an integral by reducing it to standard form by a proper substitution is called integration by substitution. If \(\phi(x)\) is continuously differentiable function, then to evaluate integrals of the form \(\int\) …
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Here you will learn what is singular matrix definition with examples and also determinant of singular matrix. Let’s begin – Singular Matrix Definition : A square matrix is a singular matrix if its determinant is zero. Otherwise, it is a non-singular matrix. Also Read : How to Find the Determinant of Matrix Example : Show …
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Here you will learn what is the matrix polynomial definition with examples. Let’s begin – Matrix Polynomial Definition : Let f(x) = \(a_0x^n\) + \(a_1x^{n – 1}\) + \(a_2x^{n – 2}\) + ……. + \(a_{n – 1}x\) + \(a_n\) be a polynomial and let A be a square matrix of order n. Then, f(A) = …
Here you will learn what is the lower triangular matrix definition with examples. Let’s begin – Lower Triangular Matrix Definition : A square matrix A = \([a_{ij}]\) is called an lower triangular matrix if \(a_{ij}\) = 0 for all i < j. Thus, in an lower triangular matrix, all elements above the main diagonal are …
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