Solve your IGNOU Doubts

Question:

(a) Find the equations of the line through (1,3, 4 ) and parallel to the line joining the points (−4, 5, 3) and (8, 9, 7).

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Question:

(d) Prove that the length of the chord of a parabola which passes through the focus and which is inclined at 30° to the axis of the parabola is four times the length of the latus rectum.

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Question:

(c) Find the eccentricity, foci, centre and directrices of the ellipse $\frac{x^2}{16}+\frac{y^2}{4}=1.$ Also give a rough sketch of it.

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Question:

(b) (i) Show that $\begin{vmatrix} x &y &1 \\2 & 3 &1 \\-4 &7 &1 \end{vmatrix}=0$ represents the equation of a line passing through (2, 3) and (−4, 7).

(ii) Prove that the equation of a line through $(x_1,y_1)$ and $(x_2,y_2)$ can be

expressed in the form $(x_2,y_2\begin{vmatrix} x & y &1 \\x_{1} &y_1 &1 \\-4 & 7 &1 \end{vmatrix}=0.$

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Question:

If A and B are the set of even integers and set of odd integers, respectively, find A ∪ B and $\left ( A\cup B \right )^{c}.$

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Question:

(a) Let See Answer →

Question:

Obtain the resolvent cubics, by Descartes’ method and by Ferrari’s method, of the equation $x^{3}+4x^{3}+8=0.$ . Are the cubics the same? Further, use either method to obtain the roots of this equation.

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Question:

Find the cubic equation whose roots are the cubes of the roots of $x^{1}+ax^{2}+bx+c=0,a,b,c \in \mathbb{R}.$

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Question:

(b) Prove that the conic passing through the points of intersection of two rectangular hyperbolas is also a rectangular hyperbola.

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Question:

(a) Trace the conic $x^2-2xy+y^2-3x+2y+3=0.$

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Question:

Check whether the following statements are true or false. Justify your answer with a short explanation or a counter example

(i) The numbers $\frac{1}{\sqrt{2}},\frac{1}{\sqrt{3}},\frac{3}{2}$ are the direction cosines of a line.

(ii) The points $(1,2),(7,6)$ and $(4,4)$ are collinear.

(iii) The conic $12x^2+12xy+3y^2+2xy=0$ is degenerate

(iv) Intersection of the ellipsoid $\frac{x^2}{4}+\frac{y^2}{25}+\frac{z^2}{4}=1$ and the plan $y=5$ is a circle. The conicoid $3x^2+y^2+2xy+x-y-z+1=0$ is non-central.