(b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. linith whether or not each of the following lines are either. +
(b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. linith whether or not each of the following lines are either. +
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Transcribed Image Text:12:46 Pf
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同
(b) Determine the slope and intercept on the coordinate axis of the equation 4x - 5y + 20 = 0. .
(c) With the aid of clear workings, state explicitly whether or not each of the following lines are either
parallel, perpendicular, or neither.
(1) y = 3x + 2 and y = 3x -2
Tii) 3x - 2y = 5 and 2x + 3y = 4
(ii) x + 3y = 1 and 4x + 2y = 3
3. (a) The tangent and normal to the parabola y² = 20x at the point 7(5.10) meet the x-axis at the point
A and 5. Show that AB2= AT2 + TB2
Given the equation of the parabola x² = -50y, find its:
(i) vertex, (ii) focus
(iii) directrix
4. (a) Show that any line passing through the point (4,-1) cannot be a tangent to the circle
x²+²-4x+6y- 12 = 0.Hence deduce the centre and radius of the circle.
22
(b) Find the length of the tangent to the circle x² +y²-3x +2y- 10 = 0 from point (-4,1).
(c) Find the equation of the tangent to the circle whose equation is x² + y²+2x-3y - 13 = 0 at point
(1.-2).
"
)
5. (a) Find an equation of an ellipse with the following conditions: foci (0, 19), length of the minor axis 24.
(b) From the equation of an ellipse 2 +9y2 + 4x + 18y-23 = 0, find the coordinate of the following
(iii) co-vertices
(iv) foci.
(i) centre (ii) vertices
6. (a) Given the equation of the hyperbola. 36x²
(i)coordinates of the center of the hyperbola
(iv) its conjugate axes and the lengths of: its transverse and conjugate axes,
(vii) its equations of the directrices and asymptotes.
(vi) its eccentricity,
(b) Find the equation of the hyperbola whose transverse axis is on the x-axis having asymptotes: y + 2x + 4 5
y-2x-4 and passes through (2, 2).
(a) 2 - 4y + 4x = 0
(b) 3x2 + 12x - 8y = 0
(c) 22x12y + 25 =0
(d) y² +4y+20x + 4 =0
e) y² = 16x
(f) ² = -9y
19. Find the equation of parabola, given
Edit
MAL. YAHAYA AJIYA (B.Sc GSU, M.Sc UNILORIN)
16. Find the equation of the tangent to cach circle through the given external point
(a) z²+²= 25, (7,1), (b) z²+y²-4x+2y-31 = 0, (-1,5) (c) ²+²=
169, (5,-12), (d) 2² + y²-4x+6y-37= 0, (3, 4).
18. Describe each of the following equations of parabola
x² = 49
-
17. Find the length of the tangent to each of the following circles.
(a) ²+² +92-11y +48 = 0, (-1,2), (b) x² + y²-2x - 4y -4 = 0, (8,10).
F(-2,0)
d:x+3=0
A
25y² = 900, Deduce the following:
(ii) its vertices
(iii) its foci
Annotate
"... 38 |
(a) V(0,0),
(b) v (0,0);
(c) V(0,0),
F(0,5)
(d) V(0,0), F on z-axis passes through (-2,6)
(e) V(1,3), F(-1,3)
T
मंत्र म
V = (0,0)
f = (a,0)
d = x=9
L = 49
■
Fill & Sign
Unsifted.
J case
Y= (0,0)
y Eo.
42249
y² = 16 ₂0
4,
f=0,9
d=y=-a
L = £49
= 16x
compare
49
Jasua
a=4.
:
4410
~= (010)
Convert
All
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