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Ans. (a) \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 \\
Explanation:
Let (x, y) be the coordinates of any point on themoving point Q.
Then we shall have
X = a cos θ \space or \space \dfrac{x}{a} = cos θ \\
X = b sin θ \space or \space \dfrac{y}{b} = sin θ \\
⇒ \dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1 \\
\left[∵ sin^2 θ + cos^2 θ =1\right]
Ans. (b) Circle
Explanation:
According to locus postulate.
Explanation:
Given, two intersecting circles with centers C and D.
AB is their common chord.
To prove : AB bisected by CD at right angles.
Proof : CA = CB (radii)
∴ C lies on the right bisector of AB. Similarly, D lies on the right bisector of AB.
Therefore, CD is the right bisector of AB.
Explanation:
Given, in quadrilateral ABCD, bisectors of ∠ B and ∠C meet in P. PM ⊥ AB and PN ⊥ CD. To prove that:
PM = PN …(i)
Construction: Draw PL ⊥ BC
Proof : P lies on bisector or of ∠B
∴ PM = PL
P lies on bisector of ∠C
PL = PN …(ii)
From (i) and (ii), we have
PM = PN.
Explanation:
Steps of construction :
(i) Draw a line AB = 5·5 cm.
(ii) Now, from point A draw ∠ XAB = 105°.
(iii) Taking A as centre and 6 cm as radius drawarc on AX mark this point as C.
(iv) Join BC.
(v) Draw bisector of ∠ ABC and perpendicularbisector of BC, both intersecting at P. P isthe required point.
Reason :
Since, (i) P is on bisector of angle ABC, P is equidistant from BA and BC.
(ii) P is on perpendicular bisector of BC, P is equidistant from B and C.
(iii) Length of PC is 5 cm.
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Download NowChapter No. | Chapter Name |
---|---|
Chapter 1 | Goods and Service Tax (GST) |
Chapter 2 | Banking |
Chapter 3 | Shares and Dividends |
Chapter 4 | Linear inequations |
Chapter 5 | Quadratic Equations in one variable |
Chapter 6 | Ratio and proportion |
Chapter 7 | Factorization |
Chapter 8 | Matrices |
Chapter 9 | Arithmetic Progression |
Chapter 10 | Geometric Progression |
Chapter 11 | Coordinate Geometry |
Chapter 12 | Reflection |
Chapter 13 | Similarity |
Chapter 14 | Loci |
Chapter 15 | Circles |
Chapter 16 | Constructions |
Chapter 17 | Mensuration |
Chapter 18 | Trigonometry |
Chapter 19 | Statistics |
Chapter 20 | Probability |
Chapter Wise Important Questions for ICSE Board Class 10 Mathematics |
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Goods and Service Tax (GST) |
Banking |
Shares and Dividends |
Linear inequations |
Quadratic Equations in one variable |
Ratio and proportion |
Factorization |
Matrices |
Arithmetic Progression |
Geometric Progression |
Coordinate Geometry |
Reflection |
Similarity |
Loci |
Circles |
Constructions |
Mensuration |
Trigonometry |
Statistics |
Probability |
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