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ignou MTE 5 solved assignment 2024

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Last Date of Submission of IGNOU MTE-05 (BSC) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Semester Wise
January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam).
July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).

Title Name	IGNOU MTE 5 Analytical Geometry Solved Assignment 2024
Type	Soft Copy (E-Assignment) .pdf
University	IGNOU
Degree	BACHELOR DEGREE PROGRAMMES
Course Code	BSC
Course Name	Bachelor in Science
Subject Code	MTE 5
Subject Name	Analytical Geometry
Year	2024
Session	-
Language	English Medium
Assignment Code	MTE-05/Assignmentt-1//2024
Product Description	Assignment of BSC (Bachelor in Science) 2024. Latest MTE 05 2024 Solved Assignment Solutions
Last Date of IGNOU Assignment Submission	Last Date of Submission of IGNOU MTE-05 (BSC) 2024 Assignment is for January 2024 Session: 30th September, 2024 (for December 2024 Term End Exam). Semester Wise January 2024 Session: 30th March, 2024 (for June 2024 Term End Exam). July 2024 Session: 30th September, 2024 (for December 2024 Term End Exam).
Assignment Code	MTE 5/2024

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Rs. 50

Questions Included in this Help Book

Ques 1.

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.

(vi) The line

Ques 2.

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

Ques 3.

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

Ques 4.

Ques 5.

(a) Let

Ques 6.

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

Ques 7.

(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.

Ques 8.

(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.

Ques 9.

(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).

Ques 10.

(b) Find the equation of the plane which passes through the line of intersection of the planes $3x+4y-5z=9$ and $2x+6y++z=7$ and which is perpendicular to the plane $3x+2y-5z+6=0.$

Ques 11.

Ques 12.

(a) Show that the plan $2x+y+2z=0$ is a tangent plane to the sphere $x^2+y^2+z^2-2x+2y-2z+2=0.$

Ques 13.

(b) Find the equation of the sphere touching the plane $8x+5y+3z+1=0$ at (3, −1, −1) and cutting the sphere $x^2+y^2+z^2-2x+y-z-6=0$ orthogonally.

Ques 14.

Ques 15.

(d) Find the equation of the cylinder with base $x^2+y^2+z62-3x-6z+9=0,x-2y+2z-6=0.$

Ques 16.

(a) Show that the perpendiculars drawn from the origin to tangent planes to the cone $x^2-y62+5z^2+4xy=0$ lie on the cone $x^2-y^2+z^2+4xy=0.$

Ques 17.

(b) Transform the equation $x^2+2y^2-6z^2-2x-8y+3=0$ by shifting the origin to (1, 2, 0) without changing the directions of the coordinate axes. What object does this new equation represent? Give a rough sketch of it.

Ques 18.

Ques 19.

(a) Examine which of the following conicoids are central and which are non-central. Also determine which of the central conicoids have centre at the origin.

(i) $x^2+y^2+x^2+4x+3y-z=0$

(ii) $2x^{2}-y^2-z^2+xy+yz-zx=1$

(iii) $x^2+y^2-z^2-2xy-3yz-6zx+x-2y+5z+4=0$

Ques 20.

(b) Find the transformation of the equation $12x^2-2y^2+z^2=2xy$ if the origin is kept fixed and the axes are rotated in such a way that the direction ratios of the new axes are 1, −3, 0; 3, 1, 0; 0, 0, 1.