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Mat 102: Analytical Geometry Question Paper
Mat 102: Analytical Geometry
Course:Bachelor Of Education (Science)
Institution: Kaimosi Friends University College question papers
Exam Year:2017
KAIMOSI FRIENDS UNIVERSITY COLLEGE
UNIVERSITY EXAMINATIONS FOR THE DEGREE OF BACHELOR OF APPLIED STATISTICS WITH IT,MATH AND ECONOMICS WITH IT,MATHEMATICS WITH IT , BACHELOR OF EDUCATION
COURSE CODE:MAT 102
COURSE TITLE: ANALYTICAL GEOMETRY
Tuesday 25th july 2017
2 Hours
INSTRUCTIONS TO CANDIDATES
Answer question ONE and any other Two questions
QUESTION ONE. 30 MARKS
a. M,N,P are three points with coordinates(1,0),(2,-4)and ( -5,-2) respectively.Determine :
i. the equation of the line through
M and perpendicular to NP. 2 marks
ii. The equation of the line through N and perpendicular to MP. 2 marks..
iii.The point of intersection of these lines. 3 marks
b. Find the equation of the circle passing through the point A(-1,-2),B(1,2) and C(2,3). 4 marks
c. The vertex of a parabola is V(5,3) and its directrix is the line y=-2
i.find it's equation. 6 Marks
ii.determine it's focus. 1 mark
d.find the equation of the normal to the ellipse 9x^2+16y^2=25 at(1,1). 3 marks
e. i). Find the equation of hyperbola With horizontal transverse axis of lengths 6,centre(2,2) and eccentricity e=2. 3 marks
ii.what is the length of the locus axis of the hyperbola. 2 marks
f. Transform the equation
I. V=12sinØ_8 cosØ into rectangular equation. 2 marks
II. X^2 +Y^2=0 into polar form.
QUESTION TWO. 20 marks
a. Find the acute the angle to the nearest 0.1^° between the pair of line L1:y=2x +3 and L2:12x -3y +7=0. 3 marks
b. The equation of a parabola is given by : y^2=-6x.
i. Determine the focus and the vertex of this parabola. 4 marks
ii. Find the directrix and eccentricity of the parabola. 3 marks
iii. Sketch the parabola. 4 marks.
c. I). Express (2,5/6p) in rectangular coordinates. 3 marks
II. Express (2,2) in a polar form. 3 marks
QUESTION THREE. 20 MARKS
a. i). Find x so that the distance between (x,3) and(2,-1) is 5. 5 marks
ii.Find the equation of the tangent to the circle x^2+y^_2x +y_5=0 at the point at (-1,1). 5 marks
b. The equation a comic section is given by x^2_4y^2+2x + 8y_7 =0
i.Show that is hyperbola 1 mark
ii. Determine its centre 1 mark
iii. Find the eccentricity and directrices. 2 marks
iv. Find the foci and vertices 2 marks
V. State the line of asymptotes 2 marks
vi. Sketch the conic section. 2 marks
QUESTION FOUR. 20 Marks
a. Transform the equation.
i.r=12sinØ_ 8cosØ into a rectangular equation. 3 marks
ii.x^2+y^2_6y =0 into polar equation. 2 marks
b. Find the equation of the normal to the ellipse 9x^2+ 16y^2=25 at( 1,1). 5 marks
c. Describe and sketch the graph of the equation 4x^2+18y^2=36
QUESTION FIVE. 20 marks
a. A conic section has the equation y=2x^2_6x+4
I. Identify the conic section the curve belongs to. 1 mark
II. Find the tangent and Normal to this curve at the point (1,2). 6 marks
b. For this curve determine
I. Vertex. 1 mark
II. Focus. 2 marks
III. Intercepts 3 marks
Iv. Directrix. 1 mark
V. Eccentricity. 1 mark
c. Sketch the graph. 5 marks
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