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• Faculty Support #### If one end of a focal chord AB of the parabola is at then the equation of the tangent to it at B is : Option: 1 Option: 2 Option: 3 Option: 4 Length of the Latus rectum and parametric form -

Parametric Equation:

From the equation of the parabola, we can write -

Tangents of Parabola in Point Form -

Tangents of Parabola in  Point Form  -   Correct Option 3

Option: 3

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• Faculty Support #### If  for  then Option: 1 Option: 2 Option: 3 Option: 4 Use

Correct Option (3)

#### If be a complex number satisfying then cannot be :  Option: 1 Option: 2 Option: 3 Option: 4 Complex number -

A complex number is the sum of a real number and an imaginary number. A complex number is expressed in standard form as a + bi where a is the real part and b is the imaginary part. For example, 5 + 2i is a complex number. So, too, is 3 + 4i√3. We write the complex number by C or z = a + ib, a and b are real number (a, b ∈ R).

• a is real part of the complex number and denoted by Re(z),

• b is the imaginary part of the complex number and denoted by Im(z),

E.g :    z = 2 + 3i is a complex number.

With Re(z) = 2 and Im(z) = 3

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Area of triangle, circle (formula) -

Equation of Circle:

The equation of the circle whose center is at the point and have radius r is given by If the center is origin then, , hence equation reduces to |z| = r

Interior of the circle is represented by The exterior is represented by Here z can be represented as x + iy and is represented by  -

z = x + iy

|x| + |y| = 4 Minimum value of |z| = Maximum value of |z| = 4 So |z| can't be Correct Option (1)

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• Faculty Support #### The length of the minor axis (along y-axis) of an ellipse in the standard form is If this ellipse touches the line, then its eccentricity is :  Option: 1 Option: 2 Option: 3 Option: 4 What is Ellipse? -

Ellipse

Standard Equation of Ellipse:

The standard form of the equation of an ellipse with center (0, 0) and major axis on the x-axis is 1. a > b

2.  the length of the major axis is 2a

3.  the coordinates of the vertices are (±a, 0)

4.  the length of the minor axis is 2b

5.  the coordinates of the co-vertices are (0, ±b)

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Equation of Tangent of Ellipse in Parametric Form and Slope Form -

Slope Form: - 