-7) 2) (3,-2) EXERCISE-2 (LOCUS) LEVEL-I us of the point, the sum of whose distances from the coordinate axes is 9 is 3) lyl- x = 9 1?) and (3,0) is 4) y+ x = 9 2) Ixl + lyl = 9 4) x + v-3.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
![quilateral triangle
ght angled triangle
o vertices o
0,10) and B = (30,20) be two points and P (x,0) be a point on the x-axis. The value
4) 10
3) 4
integral coordinates is
2)5
The
13.
1) x+2y
4) 3:4
3) 2:1
perpend
1)x
3) x+
longer side is
14 A(2.3) a
2) 4:3
a-B
15. If A=
1) x
a-p
3) cos
4) sin
a-8
2) cos
2.
V3
2
16. Let A
9x + 7
1) AB
2.
3) (-2,3)
4) (5,–1)
-7)
2) (3,-2)
17. The
The
EXERCISE-2 (LOCUS)
LEVEL-I
cus of the point, the sum of whose distances from the Coordinate axes is
1) 6
18. The
is
lyl 9
4) y + x = 9
2) |x| + ly] = 9
cus of the point equidistant from (-1,2) and (3,0) is
2) 2x-y + 1 = 0
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1)
y-1 0
3) x + y +1 = 0
4) x + y – 2 = 0
19. Le
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cus of the point which is at a constant distance of 5 from the point (2.3) is
1.
y-4x-6y-25 = 0
y²-4x-6y-8 = 0
2) x + y² – 4x - 6y + 25 = 0
4) x² + y² – 4x – 6y – 12 = 0
20. If
is
-y 0
us of the point P from which the distance to (4,0) is double the distance from P to
is
By2-8x+16 0
y - 8y + 16 = 0
us of the point P which moves such that its distance from (4,0) is twice its distance
line x = 1 is
By 12
9,0) and B (-1,0) then the locus of P such that PA = 3PB is
2) x- 3y² = 0
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3) 3x? - y = 0
%3D
4) x²– 2y² = 0
%3D
%3D
21.
%3D
2) x²- 3y² - 8x- 16 = 0
4) 3x -y-8y- 16 = 0
22.
%3D
%3D
%3D
2) 3x- y = 12
23
%3D
3) x + 3y? = 12
2) y -x = 9
4) 3x² + y = 12
%3D
%3D
3) x² + y² = 9
%3D
which the sum of the distance of P from A andB is minimum equals
2
%3D
4) x² - y²+9 = 0
2)20
a
enal Institutes
3) 15
4)0
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